I am assuming this is for CA 2E.
What type of function is it?
For the existing functions that call this function you are changing is the new parameter passed with a default value or blank/zero?
If the function is an EXCINTFUN or EXCEXTFUN - then it is easy to fix by adding another layer in the call path.
1. Copy the existing function to a new function - if the function is an EXCEXTFUN - then change function type to EXCINTFUN.
2. Change the new EXCINTFUN to have the new parameter(s).
3. Edit the original function and remove all the logic (or comment it out if you want to play it safe). Then insert a call to the new EXCINTFUN function and default the new parameters as you require them.
4. Change the name of the old function to indicate that it is no longer to be used and that the new EXCINTFUN function is to be used instead.
For other types of functions - then I would do something similar - I would copy the function to a new function and not change the function type - add the new parameter(s) to the new function - I would then edit the internals to change the function type of the original function to an EXCINTFUN.
Changing internals is not advised if you are not an expert in understanding the internal file structures - as it is not just a simple change to one field in one file - you need to make sure you do not corrupt the data model and take into consideration any change management tools you might be using. So I will not be providing any details on how to do this step here.