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That doesn't answer his very specific question.

This thread is giving me a flashback to Stack Overflow

I think I might have just misunderstood his question then. I assumed the limitations come from the subscription plan

It's actually fairly easy to setup a 3rd party app to use Claude via API, to get extremely generous limits.

I wrote a step-by-step guide for the app I built: https://prompt.16x.engineer/guide/claude