If there are hooks in the function, this is possible, if not, there may be pluggable functions, where you can replace their function with your own custom function. I have not seen pluggables in plugins frequently, but with most of the more popular plugins, you do see actions and filters.
You may be able to interact with the plugin by changing the behavior of the functions which it calls to your desired effect. This can be tricky, and often results in hacky solutions, but it’s better than nothing.
If there is not a way to interact with the plugin, then you can fork the plugin’s code. Naturally, this is the least desirable, but it may be your only option.