Depends on *how much* it’s pushed past its terminal velocity. As others have mentioned, if it’s only pushed a little bit past the terminal velocity, then the object reaches a new point at which the forces balance, and then it stops accelerating again (and returns to terminal velocity once the extra force is removed.)
However, if it’s pushed waaayyyy past terminal velocity, the picture gets a lot more interesting, as illustrated by the [xccd relativistic baseball](https://what-if.xkcd.com/1/)
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