Generally, the installation needs to be on your main hard drive.

While the data files could go on another drive, I think the data files are fairly small.

Fifteen years?  Do you EVER go back more than six years?  If not, uninstall the older versions.

Hard drives are fairly low-cost; you would be better off finding someone that could transfer EVERYTHING to a new, larger internal hard drive.  Or if your computer is fairly old, replace your computer and make sure your new computer has a larger hard drive.

I have done that with ProSeries before and moving the program to an externs drive does not work very well. It relies on some system files and registry entries that don't transfer over. It will open, but it glitches or freezes or crashes. 

The better way to do it is to back up your older data files on a portable drive, then uninstall the older ProSeries years you do not use. This maintains a lighter system, with your older work still being held safely.