Since no one else has answered, I’ll try to point you in a useful direction, at least, though I can’t really be much more helpful. A piecewise model of some kind might be a way to model an effect reaching a plateu, as you describe. I’d suggest you have a look at this thread, which might be a good place to start (if you haven’t already): Piecewise Linear Mixed Models With a Random Change Point
Apart from that, it might be helpful to share a bit more about your data and what process you are trying to model, and for what purpose?