Rest assured prematurely access response stream

I need to verify a text/event-stream response for its content up to a certain point in time after the request was sent. The response stream is kept alive indefinitely for new events.

The following code does not work:

given()
    .contentType(JSON)
    .when()
    .get("/mypath/") // This method blocks indefinitely, never reaching the "then" block
    .then()
    .response()
    .extract()
    .asString()

How can we close the response stream at a certain point to access what it has so far? Or perhaps intercept the underlying InputStream of the response asynchronously somehow?