If your hardware can support it you should be able to run every antivirus, antispyware, antimalware anti-whatever available.. The issue is with real-time scanning & how they embed with Windows to do that and how they interact with each other not only during scanning of clean files but especially infected ones. If you only had 1 real-time & 20 on-demand only scanners that you ran as needed I doubt it'd ever be an issue although I've heard of them detecting each other and 'add-on' things like firewalls & heuristics & such causing grief when running more than 1.
On top of the huge possibility of conflict you have to ask if you really need more than 1 scanner. In your case sounds like the 2 compliment each other rather than replace (likely some redundancy but not too bad) so odds are they should be fine but as matt said check with both to see if there are any known issues or give them a try & watch carefully for issues.
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