Swagger; specify two responses with same code based on optional parameter

OpenAPI 2.0

OAS2 does not support multiple response schemas per status code. You can only have a single schema, for example, a free-form object (type: object without properties).

OpenAPI 3.x

In OAS3 you can use oneOf to define multiple possible request bodies or response bodies for the same operation:

openapi: 3.0.0
...
paths:
  /path:
    get:
      responses:
        '200':
          description: Success
          content:
            application/json:
              schema:
                oneOf:
                  - $ref: '#/components/schemas/ResponseOne'
                  - $ref: '#/components/schemas/ResponseTwo'

However, it's not possible to map specific response schemas to specific parameter values. You'll need to document these specifics verbally in the description of the response, operation and/or parameter.

Here's a possibly related enhancement request:
Allow operationObject overloading with get-^ post-^ etc

Note for Swagger UI users: Older versions of Swagger UI (before v. 3.39.0) do not automatically generate examples for oneOf and anyOf schemas. As a workaround, you can specify a response example or examples manually. Note that using multiple examples require Swagger UI 3.23.0+ or Swagger Editor 3.6.31+.

      responses:
        '200':
          description: Success
          content:
            application/json:
              schema:
                oneOf:
                  - $ref: '#/components/schemas/ResponseOne'
                  - $ref: '#/components/schemas/ResponseTwo'
              example:   # <--- Workaround for Swagger UI < 3.39.0
                foo: bar