You can. But if you cannot have another person using the program at the same time you are using CS4. You can even have CS4 on two computers, as long as it is only one user at a time.
Many people keep both CS3 and CS4 on their computers because they might need to fall back to the older system because of a bug (when the program is new) or because they can do something quicker in the old version, at a later time.
I have to keep CS2. The CS4 I bought a month ago still crashes even with the few recent updates. Never "upgrade" too quickly any more, you might regret it.
Robert, your constant hijacking of posts is becoming very tiring.
If you have nothing useful to add, please can it.
Bob