How do I override a function in a module I want to batch override (there are hundreds of terms) menu paths generated by the Taxonomy Menu module for a custom menu I require.  I know not to edit the module itself. I assume I create a separate module containing the replacement function to substitute the desired path I want, but I am not certain how to direct Drupal to use it instead of the original.  Or am I using the wrong strategy for this?

UPDATE:
I have solved the specific example in the question using a panel tied to a view. However, I am still interested in the question itself. A theme function can be overridden by including the replacement function with my theme name replacing the original theme name in the function name. Drupal handles the substitution from there; the same renaming option is not available for module functions.

I have continued to research this and found several posts at Drupal.org, that suggests it is not possible to override module functions in the same way you override theme functions.  There was a module for this in Drupal 6 (Override_Function), but it required additional software and appeared to have some problems working with PHP 5.2 &amp; 5.3. The only workaround I have found so far is to hack it, but keep track of your changes so that it can be reinserted after updates.
It sounds more like you want to use hook_menu_alter to override what the Taxonomy Menu module's hook_menu function does.