Theoreticall, the developers of anti-virus software have a tacit agreement between each other not to identify the competitors' files as malware or whatever.
However, in real life, this rule gets broken sometimes. I've heard quite a lot of stories about bloodbaths and horrible wars waged by anti-viruses against each other when installed on one machine.
On the other hand, having two anti-viruses installed is a good idea, since some of them (in fact, as good as all) do not scan their own directories. It means that if a malicious file lands into the directory of the only anti-virus program, installed on your computer, you'll be most likely screwed.
I would use the second anti-virus purely for scanning the directory of the first one. Call it paranoia, call it schizophrenia, call it whatever, butthat's what I would do.