You cannot, and the maximum number of results returned is still limited by limit (default 25, max 100), so the list for a single request cannot be ‘ever growing’.
Additionally, the reason why this isn’t feasible is because a GET request cannot contain a body. Twitch would have to adjust their API structure endpoints considerably for this to be accepted (e.g. use POST requests), and this doesn’t seem to match their intended API structure.
Even if they did do this, though, they would still have a limit on the response size of the HTTP request to make sure that no single user is hogging the servers by making inefficient, large requests. You’ll have to structure your requests accordingly to work around this fact.