AppFS ( http://appfs.rkeene.org/ ) solves this (and all other packaging and distribution problems) by dividing the namespace along DNS lines.

That is you can run both:

     /opt/appfs/linuxmint.com/mdm/platform/latest/bin/mdm

and

     /opt/appfs/debian.org/mdm/platform/latest/bin/mdm

They are both always accessible (in other packaging systems you would refer to them as a "installed" since all their files may be read).