In the simplest scenario where each distribution has its own partition and everything necessary for the system to run is within that partition (you don't have separate partitions for /usr for example), you can do this with chroot:
I assume you have the partitions mounted somewhere, let's say they're at /Debian and /Fedora. Set up a chroot environment:
sudo chroot /Debian
That will move you into /Debian, running a shell that thinks you are root and running the installed Debian system. At this point, you can use apt-get as you would normally. When you're done, you can return to your session by running exit.
This should work perfectly well for simple software management but I wouldn't run major updates or changes to important packages this way.
/etc,/usretc on the same partition) it is very easy to do withchroot. – terdon Jan 03 '14 at 01:58chrootsuggestion should work for most use cases. – terdon Jan 03 '14 at 13:07