The answer is yes but probably not the way you have in mind.
General steps are, say you have a Linux in sda7 and want to move it to sdc2
Boot up a Linux not related to the one you want to migrate, in terminal
mount /dev/sdc2 /mnt/sdc2
mount /dev/sda7 /mnt/sda7
tar cf - . | (cd /mnt/sdc2; tar xf -)
go into /mnt/sdc2 and change
(1) boot loader reference from sda7 to sdc2
(2) /etc/fstab same alteration
(3) Restore the boot loader (only if you boot by chainloading)
All Linux should use a common swap.
/mnt cannot be shared.
Sharing a /home between Linux may upset the desktop setting.
Yes you can move Linux around. I do it all the time.