I have downloaded an earlier version of the Design Suite (CS4) on two Mac computers and recently I upgraded to 5.5 on one of them - how do I upgrade the other one?
For each release you are allowed to install on up to two systems, and with upgrades you're fine so long as those are the same two.
So, just install CS5.5 on your other machine and you're good. The installer will find the earlier version already on there, and complete.