By TMI are you referring specifically to chat connections or some of the undocumented TMI API endpoints?
If you’re referring to chat then there’s docs on Chat Limits.
If you’re on about using undocumented TMI API endpoints then as they are not documented those endpoints can and will change/break at any time without warning in the future, and as for limits then there are no specific hard limits, it’s more a case of if you use an API excessively then yes it’s reasonable to assume Twitch will block you and attempt to get in contact with you. As to what’s ‘excessive’ there’s not strict definition but just use common sense, for example the API results are cached so hitting the same endpoint more frequently than once a minute is unlikely to get you anywhere other than waste your own resources, and if you’re making tens/hundreds of thousands of requests a minute then you should probably have a use case for doing so. Again, there’s no specific docs or guidance other than use common sense and you’ll be fine.
Also, Twitch don’t charge for any of their developer services. If you’re hitting rate limits then you can use Twitch’s Limit Increase form with details about what limit you need increasing and your apps justification for needing a higher limit and if they feel there is sufficient need to increase your rate limit they will do so, free of any charge