diff --git a/README.md b/README.md
index e5d11d12..975a64b2 100644
--- a/README.md
+++ b/README.md
@@ -45,7 +45,7 @@ npm run build        # writes dist/ and regenerates index.html; the folder is wh
 The browser suite and the three example games need a machine with a GPU:
 
 ```bash
-node tools/seed-e2e.mjs && node tools/e2e.mjs      # the editor, 1671 checks (GM_STEPS=20 for one step)
+node tools/seed-e2e.mjs && node tools/e2e.mjs      # the editor, 1673 checks (GM_STEPS=20 for one step)
                                                    #   every tool signs in first – see the Accounts page
 node tools/seed-jumprun.mjs && node tools/smoke-jumprun.mjs
 node tools/seed-tetris.mjs && node tools/smoke-tetris.mjs
diff --git a/src/core/graph/nested.ts b/src/core/graph/nested.ts
index ce80ce91..696e7322 100644
--- a/src/core/graph/nested.ts
+++ b/src/core/graph/nested.ts
@@ -145,7 +145,7 @@ export function declaredPorts(graph: Graph | undefined, type: string): PortDef[]
  * type declares ports per node (`declaresPorts`) or computes them (`derivePorts`).
  */
 export function resolveDef(node: GraphNode, graph: Graph, lookup: GraphLookup): NodeDef | undefined {
-  const def = shapedDef(node, graph, lookup, true);
+  const def = shapedDef(node, graph, lookup, newTrail());
   return def && splitDef(def, node);
 }
 
@@ -158,24 +158,41 @@ function splitDef(def: NodeDef, node: GraphNode): NodeDef {
  * produces its wholes as always; reading a field port picks the field out of one (`splitField`).
  */
 export function runDef(node: GraphNode, graph: Graph, lookup: GraphLookup): NodeDef | undefined {
-  return shapedDef(node, graph, lookup, true);
+  return shapedDef(node, graph, lookup, newTrail());
 }
 
 /**
- * `inherit` is off while answering what feeds a shared group: a node of that kind then reports the
- * `any` it was registered with, so two of them in a row cannot ask each other in circles (#207).
+ * One question about a shared group, followed through the nodes of that kind in front of it (#210).
+ * `open` holds the nodes still being asked: reaching one again is a data cycle, and it then reports
+ * the `any` it was registered with, which ends the circle. `done` keeps each answer, so a node
+ * feeding both inputs of the next is asked once and not once per path.
  */
-function shapedDef(
-  node: GraphNode,
-  graph: Graph,
-  lookup: GraphLookup,
-  inherit: boolean,
-): NodeDef | undefined {
+interface Trail {
+  open: Set<string>;
+  done: Map<string, NodeDef>;
+}
+
+function newTrail(): Trail {
+  return { open: new Set(), done: new Map() };
+}
+
+function shapedDef(node: GraphNode, graph: Graph, lookup: GraphLookup, trail: Trail): NodeDef | undefined {
   const def = nodeDef(node.type);
   if (!def) return undefined;
-  const shared = inherit ? def.sharedType : undefined;
-  if (!def.declaresPorts && !def.derivePorts)
-    return shared ? withSharedType(def, shared, node, graph, lookup) : def;
+  const shared = def.sharedType;
+  if (!shared || trail.open.has(node.id)) return ownShape(def, node, graph, lookup);
+  const known = trail.done.get(node.id);
+  if (known) return known;
+  trail.open.add(node.id);
+  const typed = withSharedType(ownShape(def, node, graph, lookup), shared, node, graph, lookup, trail);
+  trail.open.delete(node.id);
+  trail.done.set(node.id, typed);
+  return typed;
+}
+
+/** The ports of this node before any shared group has its say. */
+function ownShape(def: NodeDef, node: GraphNode, graph: Graph, lookup: GraphLookup): NodeDef {
+  if (!def.declaresPorts && !def.derivePorts) return def;
   const own = (side: 'inputs' | 'outputs') =>
     declaredOn(def, node.ports ?? [], side).map((p) =>
       def.declaredPort ? def.declaredPort(p, node, graph, lookup) : portDefOf(p),
@@ -185,13 +202,12 @@ function shapedDef(
     const ports = [...def[key], ...(grown[key] ?? []), ...own(key)];
     return grown.inOrder ? ports : execFirst(ports);
   };
-  const resolved = {
+  return {
     ...def,
     label: grown.label ?? def.label,
     inputs: side('inputs'),
     outputs: side('outputs'),
   };
-  return shared ? withSharedType(resolved, shared, node, graph, lookup) : resolved;
 }
 
 /** The group's outputs, retyped to what its inputs agree on; `any` leaves the definition alone. */
@@ -201,8 +217,9 @@ function withSharedType(
   node: GraphNode,
   graph: Graph,
   lookup: GraphLookup,
+  trail: Trail,
 ): NodeDef {
-  const type = agreedType(group.inputs.map((key) => feedingType(node, key, graph, lookup, false)));
+  const type = agreedType(group.inputs.map((key) => feedingType(node, key, graph, lookup, trail)));
   if (type === 'any') return def;
   return {
     ...def,
@@ -211,21 +228,20 @@ function withSharedType(
 }
 
 /**
- * What the edge into that input carries, or undefined while nothing is connected to it. `inherit`
- * says whether a shared group on the *feeding* node may have its say: off while a group asks what
- * feeds it, on when only the drawn colour is wanted, which is what the edge itself is drawn in.
+ * What the edge into that input carries, or undefined while nothing is connected to it: the type
+ * the feeding node resolves to, which is what the edge itself is drawn in.
  */
 function feedingType(
   node: GraphNode,
   key: string,
   graph: Graph,
   lookup: GraphLookup,
-  inherit: boolean,
+  trail: Trail,
 ): PortType | undefined {
   const edge = edgesInto(graph, node.id, key)[0];
   if (!edge) return undefined;
   const from = findNode(graph, edge.from.node);
-  const def = from && shapedDef(from, graph, lookup, inherit);
+  const def = from && shapedDef(from, graph, lookup, trail);
   return def && splitDef(def, from).outputs.find((p) => p.key === edge.from.port)?.type;
 }
 
@@ -236,9 +252,10 @@ function feedingType(
  */
 function paintedInputs(node: GraphNode, graph: Graph, def: NodeDef, lookup: GraphLookup): PortDef[] | null {
   if (!def.inputs.some((port) => port.type === 'any' && !port.ghost)) return null;
+  const trail = newTrail();
   return def.inputs.map((port) => {
     if (port.type !== 'any' || port.ghost) return port;
-    const fed = feedingType(node, port.key, graph, lookup, true);
+    const fed = feedingType(node, port.key, graph, lookup, trail);
     return fed === undefined || fed === 'any' || fed === 'exec' ? port : { ...port, paintType: fed };
   });
 }
diff --git a/tests/core/shared-port-type.test.ts b/tests/core/shared-port-type.test.ts
index 2657136f..bd183c1e 100644
--- a/tests/core/shared-port-type.test.ts
+++ b/tests/core/shared-port-type.test.ts
@@ -100,21 +100,6 @@ describe('First not empty, whose a, b and value carry the same value', () => {
     expect(may).toBe(true);
   });
 
-  it('does not pass the type on through a second one of its kind', () => {
-    const f = fixture();
-    const first = f.edit.addNode('FirstNotEmpty');
-    const second = f.edit.addNode('FirstNotEmpty');
-    f.edit.wire([
-      [f.edit.addNode('Number'), 'value', first, 'a'],
-      [f.edit.addNode('Number'), 'value', first, 'b'],
-      [first, 'value', second, 'a'],
-      [first, 'value', second, 'b'],
-    ]);
-    expect(typeOf(f.behavior, first, 'value', f)).toBe('number');
-    // A chain would have to resolve its neighbour to answer, and two of them would ask in circles.
-    expect(typeOf(f.behavior, second, 'value', f)).toBe('any');
-  });
-
   it('leaves an edge that the new type makes invalid in place, for the canvas to mark', () => {
     const f = fixture();
     const node = f.edit.addNode('FirstNotEmpty');
@@ -167,6 +152,184 @@ describe('Select, whose false, true and value carry the same value', () => {
   });
 });
 
+type Fixture = ReturnType<typeof fixture>;
+
+/** `count` First not empty in a row: the first fed by two literals, each next one by the one before. */
+function chain(f: Fixture, count: number, literal: string, kind = 'FirstNotEmpty'): GraphNode[] {
+  const [a, b] = kind === 'Select' ? ['false', 'true'] : ['a', 'b'];
+  const nodes = Array.from({ length: count }, () => f.edit.addNode(kind));
+  f.edit.connect(f.edit.addNode(literal), 'value', nodes[0]!, a);
+  f.edit.connect(f.edit.addNode(literal), 'value', nodes[0]!, b);
+  for (let i = 1; i < count; i++) {
+    f.edit.connect(nodes[i - 1]!, 'value', nodes[i]!, a);
+    f.edit.connect(nodes[i - 1]!, 'value', nodes[i]!, b);
+  }
+  return nodes;
+}
+
+/** Two First not empty feeding each other, each with a number on its other input. */
+function circle(f: Fixture): [GraphNode, GraphNode] {
+  const first = f.edit.addNode('FirstNotEmpty');
+  const second = f.edit.addNode('FirstNotEmpty');
+  f.edit.wire([
+    [f.edit.addNode('Number'), 'value', first, 'b'],
+    [f.edit.addNode('Number'), 'value', second, 'b'],
+    [first, 'value', second, 'a'],
+    [second, 'value', first, 'a'],
+  ]);
+  return [first, second];
+}
+
+describe('a type handed on through several nodes with a shared group (#210)', () => {
+  it('reaches the second node of a chain', () => {
+    const f = fixture();
+    const [first, second] = chain(f, 2, 'Number');
+    expect(typeOf(f.behavior, first!, 'value', f)).toBe('number');
+    expect(typeOf(f.behavior, second!, 'value', f)).toBe('number');
+  });
+
+  it('reaches the third, and keeps every input on the way any', () => {
+    const f = fixture();
+    const nodes = chain(f, 3, 'String');
+    expect(nodes.map((n) => typeOf(f.behavior, n, 'value', f))).toEqual(['string', 'string', 'string']);
+    expect(nodes.map((n) => typeOf(f.behavior, n, 'a', f, 'inputs'))).toEqual(['any', 'any', 'any']);
+  });
+
+  it('passes from one kind of node to another', () => {
+    const f = fixture();
+    const [pick] = chain(f, 1, 'Animation');
+    const select = f.edit.addNode('Select');
+    f.edit.wire([
+      [pick!, 'value', select, 'false'],
+      [f.edit.addNode('Animation'), 'value', select, 'true'],
+    ]);
+    const animation = typeOf(f.behavior, pick!, 'value', f);
+    expect(animation).not.toBe('any');
+    expect(typeOf(f.behavior, select, 'value', f)).toBe(animation);
+  });
+
+  it('is any behind a node whose inputs disagree, and untouched in front of it', () => {
+    const f = fixture();
+    const nodes = chain(f, 4, 'Number');
+    // The second node now hears a number and a text.
+    f.edit.connect(f.edit.addNode('String'), 'value', nodes[1]!, 'b');
+    expect(nodes.map((n) => typeOf(f.behavior, n, 'value', f))).toEqual(['number', 'any', 'any', 'any']);
+  });
+
+  it('is any behind a node with an input left open', () => {
+    const f = fixture();
+    const first = f.edit.addNode('FirstNotEmpty');
+    const second = f.edit.addNode('FirstNotEmpty');
+    f.edit.wire([
+      [f.edit.addNode('Number'), 'value', first, 'a'],
+      [first, 'value', second, 'a'],
+      [first, 'value', second, 'b'],
+    ]);
+    expect(typeOf(f.behavior, second, 'value', f)).toBe('any');
+  });
+
+  it('falls back to any all along the chain when an edge at its front is undone', () => {
+    const f = fixture();
+    const nodes = Array.from({ length: 3 }, () => f.edit.addNode('FirstNotEmpty'));
+    f.edit.wire([
+      [nodes[0]!, 'value', nodes[1]!, 'a'],
+      [nodes[0]!, 'value', nodes[1]!, 'b'],
+      [nodes[1]!, 'value', nodes[2]!, 'a'],
+      [nodes[1]!, 'value', nodes[2]!, 'b'],
+      [f.edit.addNode('Number'), 'value', nodes[0]!, 'a'],
+      [f.edit.addNode('Number'), 'value', nodes[0]!, 'b'],
+    ]);
+    expect(nodes.map((n) => typeOf(f.behavior, n, 'value', f))).toEqual(['number', 'number', 'number']);
+
+    f.stack.undo();
+    expect(nodes.map((n) => typeOf(f.behavior, n, 'value', f))).toEqual(['any', 'any', 'any']);
+
+    f.stack.redo();
+    expect(nodes.map((n) => typeOf(f.behavior, n, 'value', f))).toEqual(['number', 'number', 'number']);
+  });
+
+  it('ends a circle of two with any instead of asking forever', () => {
+    const f = fixture();
+    const [first, second] = circle(f);
+    expect(typeOf(f.behavior, first, 'value', f)).toBe('any');
+    expect(typeOf(f.behavior, second, 'value', f)).toBe('any');
+  });
+
+  it('ends a node feeding itself with any', () => {
+    const f = fixture();
+    const node = f.edit.addNode('FirstNotEmpty');
+    f.edit.connect(f.edit.addNode('Number'), 'value', node, 'b');
+    // No command lays this edge, a file written by hand can still carry it.
+    f.behavior.graph.edges.push({
+      id: 'loop',
+      from: { node: node.id, port: 'value' },
+      to: { node: node.id, port: 'a' },
+    });
+    expect(typeOf(f.behavior, node, 'value', f)).toBe('any');
+  });
+
+  it('is any behind a circle as well', () => {
+    const f = fixture();
+    const [, second] = circle(f);
+    const behind = f.edit.addNode('FirstNotEmpty');
+    f.edit.wire([
+      [second, 'value', behind, 'a'],
+      [f.edit.addNode('Number'), 'value', behind, 'b'],
+    ]);
+    expect(typeOf(f.behavior, behind, 'value', f)).toBe('any');
+  });
+
+  it('makes an edge further down the chain invalid, and leaves it in place', () => {
+    const f = fixture();
+    const first = f.edit.addNode('FirstNotEmpty');
+    const second = f.edit.addNode('FirstNotEmpty');
+    const sub = f.edit.addNode('Substring');
+    f.edit.wire([
+      [second, 'value', sub, 'text'],
+      [first, 'value', second, 'a'],
+      [first, 'value', second, 'b'],
+    ]);
+    const lookup = () => graphLookup(f.project);
+    const out = () =>
+      portTypeOf(f.behavior.graph, { nodeId: second.id, port: 'value', isOutput: true }, lookup())!;
+    const inp = () =>
+      portTypeOf(f.behavior.graph, { nodeId: sub.id, port: 'text', isOutput: false }, lookup())!;
+    expect(portsCompatible(out(), inp())).toBe(true);
+
+    f.edit.wire([
+      [f.edit.addNode('Number'), 'value', first, 'a'],
+      [f.edit.addNode('Number'), 'value', first, 'b'],
+    ]);
+    expect(portsCompatible(out(), inp())).toBe(false);
+    expect(f.behavior.graph.edges.filter((e) => e.to.node === sub.id)).toHaveLength(1);
+  });
+
+  it('asks a node feeding both inputs of the next only once, however long the chain', () => {
+    const f = fixture();
+    // Asked once per path, the last of 40 would be asked 2^40 times and this test would never end.
+    const nodes = chain(f, 40, 'Number', 'Select');
+    expect(typeOf(f.behavior, nodes[39]!, 'value', f)).toBe('number');
+  });
+
+  it('resolves every node of a chain of 50 well within a frame', () => {
+    const f = fixture();
+    const nodes = chain(f, 50, 'Number');
+    const lookup = graphLookup(f.project);
+    const all = () => {
+      for (const node of f.behavior.graph.nodes)
+        drawnDef(node, f.behavior.graph, resolveDef(node, f.behavior.graph, lookup)!, lookup);
+    };
+    all();
+    const start = performance.now();
+    for (let i = 0; i < 20; i++) all();
+    const each = (performance.now() - start) / 20;
+    expect(typeOf(f.behavior, nodes[49]!, 'value', f)).toBe('number');
+    // What the canvas does on every change to the project. Measured at 10 ms on the slowest host,
+    // against 2 ms before chains; the bound only has to catch a walk that grows with every path.
+    expect(each).toBeLessThan(200);
+  });
+});
+
 /** As the canvas draws it: `drawnDef` is the only place a pin colour is decided. */
 const inputPin = (behavior: BehaviorAsset, node: GraphNode, key: string, f: ProjectFixture): PortDef => {
   const lookup = graphLookup(f.project);
@@ -223,11 +386,25 @@ describe('an any input painted as what flows into it', () => {
       [f.edit.addNode('Number'), 'value', first, 'b'],
       [first, 'value', second, 'a'],
     ]);
-    // The edge is drawn in number, so the pin it ends on is too – the type is not passed on.
+    // The edge is drawn in number, so the pin it ends on is too. Its other input is still open.
     expect(inputPin(f.behavior, second, 'a', f).paintType).toBe('number');
     expect(typeOf(f.behavior, second, 'value', f)).toBe('any');
   });
 
+  it('follows a type handed on through a chain, two nodes back', () => {
+    const f = fixture();
+    const nodes = chain(f, 3, 'Number');
+    expect(inputPin(f.behavior, nodes[2]!, 'a', f).paintType).toBe('number');
+    expect(inputPin(f.behavior, nodes[2]!, 'b', f).paintType).toBe('number');
+  });
+
+  it('stays grey on every pin of a circle', () => {
+    const f = fixture();
+    const [first, second] = circle(f);
+    expect(inputPin(f.behavior, first, 'a', f).paintType).toBeUndefined();
+    expect(inputPin(f.behavior, second, 'a', f).paintType).toBeUndefined();
+  });
+
   it('leaves an input with a type of its own alone', () => {
     const f = fixture();
     const sub = f.edit.addNode('Substring');
diff --git a/tools/e2e/06-graph.mjs b/tools/e2e/06-graph.mjs
index 216f77d1..1914b7ce 100644
--- a/tools/e2e/06-graph.mjs
+++ b/tools/e2e/06-graph.mjs
@@ -1050,6 +1050,41 @@ export async function graph(t) {
     JSON.stringify({ pinColors, wanted }),
   );
   await shot('20-input-pin-colours');
+
+  // A second node of the kind behind the first (#210): the type is handed on through the chain,
+  // and taken back all along it once the front of the chain disagrees again.
+  await mutate(`
+    __gm.state.project.assets
+      .find((a) => a.id === 'picky')
+      .graph.nodes.push({ id: 'p-next', type: 'FirstNotEmpty', x: 300, y: 330, params: {} });
+  `);
+  const nextTypes = async () => json(`__gm.graph.portTypes('p-next')`);
+  await wire('p-pick', 'value', 'p-next', 'a');
+  await wire('p-pick', 'value', 'p-next', 'b');
+  const chainOpen = await nextTypes();
+  await wire('p-a', 'value', 'p-pick', 'a');
+  const chainTyped = await nextTypes();
+  check(
+    'a second node of the kind behind the first takes the type the first one agreed on',
+    chainOpen.outputs.value === 'any' &&
+      (await pickTypes()).outputs.value === 'number' &&
+      chainTyped.outputs.value === 'number' &&
+      chainTyped.inputs.a === 'any' &&
+      chainTyped.paint.a === 'number' &&
+      chainTyped.paint.b === 'number',
+    JSON.stringify({ chainOpen, chainTyped }),
+  );
+  await shot('20b-shared-type-chain');
+  await wire('p-text', 'value', 'p-pick', 'a');
+  const chainMixed = await nextTypes();
+  check(
+    'a text plugged into the first opens the whole chain up again',
+    (await pickTypes()).outputs.value === 'any' &&
+      chainMixed.outputs.value === 'any' &&
+      chainMixed.paint.a === 'any' &&
+      chainMixed.paint.b === 'any',
+    JSON.stringify(chainMixed),
+  );
   await mutate(`
     const p = __gm.state.project;
     p.assets = p.assets.filter((a) => a.id !== 'picky');