Black and white? Or colour?
When push processing (or 'pushing') a film you are pretending that it has a higher ISO rating than it actually has. This is actually under-exposing and over-developing.
The practical limit for B&W is about 3 stops, colour barely one.
Why colour film doesn't push well is because you have three film layers, each one sensitive to a different colour of light, and pushing tends to make the layers respond differently. Push too far and you can get crossed curves - highlights go magenta and shadows cyan. Impossible to filter out.
B&W is much better.
Problems: fairly low shadow contrast, high highlight contrast (resulting in a general increase in overall contrast), higher average density, higher fog level, increase in grain.
These problems get worse the more you push the film.
If you push too far you start losing shadow detail because there isn't enough light getting to the film to get an exposure.
Processing is a bit rule of thumb. A good place to start is increasing development 15 to 20% for each stop increase.
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