welcome to the forums, kedavra.

the quick answer is yes... you can multi-box any number of classes... technically. the trick, as you mentioned, is figuring out the key sequences with a limited keyboard.

if you are just starting out, i would recommend rolling a set of warlocks and running them to 30+. casters are easier to multi-box then melee... omni-directional casters are easiest of all. it's still complex to track, but at least you removed some of the issues you'd face with 3 different classes on your first go-round.