Even better is ... just not breaking the interface, leave the code be.
Add parameters at the end. Or just add a new function. Or even a new module if things get too messy for your liking.
Just leave the old users in peace. If you are worried about breaking stuff, it means people are using the function you wrote and find value in it. Why change it at all? I think it is very rare that the reasons for breaking are so compelling that they are worth the trouble.