It's not really going to increase your protection level, and most likely the two are going to fight with one another over who gets to scan the files being accessed.
Not to mention anti-virus vendors of late have decided that they're each going to name every new virus/worm something different, so they both might come up saying they've detected a different virus/worm in the same file, when it's really the same one.
Just pick one and stick with it.
Can one have two virus scanners going at the same time?
I presently have Norton 2003 and would like to add AVG virus scanner also for more protection.