It would take gpt-4 far over a minute to generate 10000 output tokens, so the issue is likely how much input you are providing that counts towards the token per minute count.
Consider: if you send 6000 tokens of input (and even get a quick short answer), you can’t do that again in the same minute.
Rate increase requests can be made, but approval probably needs a company, a desired application of AI, and payment history (and gpt-4 capacity).