In general, pushing is meant to compensate for underexposure, not overexposure. If you overexpose color film and then push-process it, the effects tend to work against each other rather than giving you the “best of both.”

Overexposure can help record more shadow detail on color negative film, but push processing (overdevelopment) increases contrast and grain and can reduce detail in areas that were already well exposed. With overexposed frames, that often means harsher contrast, coarser grain, and weaker highlight detail—sometimes giving washed-out or blown-looking highlights rather than a balanced negative.

So the trade-off is usually: possible shadow information from the extra exposure, but at the cost of more grain, more contrast, and less smooth highlight tonality. If the film was truly overexposed, the more typical lab correction would be pull processing rather than push processing.

Also, color film is generally less forgiving of push/pull changes than black-and-white if your goal is neutral, accurate tonality. You can still do it for a creative look, but it’s more of an effect than a way to improve image quality.