maximum output of a LTI system within linear limits
For a given LTI system, …, after which it becomes non linear


never. If you're modeling a system to be LTI, it's LTI: Linear (and time-invariant).

You can of course model a system to be non-linear in general, but linear for a range  of input. But then the answer to your question is "that's in your own model, and we can't tell you"!