Executing command while copying

Out of curiousity, is it possible to somehow execute an external command instead of just copying a file from one folder to the next.

For example, say I have a directory tree of my own MP3s, encoded in a high quality format, but want to duplicate that directory structure in another subdirectory, but, instead of just copying the files, I want to run them through an encoder to resample/reduce the quality/size of those files.

Possible? Suggestions?

Thanks in advance.