Depending on the virus checkers, you can run two or more simultaneously, which I've already seen people do successfully or without realising. However, assuming they don't conflict, the consequence is that it will most likely cause a noticeable slow down, much like having a second security screening at an airport.
As you are just looking to run one at a time, the best thing in my opinion would be to find a good real-time AV and find a standalone AV that you can run on demand. For example, Microsoft Security Essentials for a real-time AV and ClamAV for an on-demand check (both free).
This AV review is worth a look at, which compares 15 in real-life tests on Malware infected websites with PCs missing updates and using old version of Flash, Java, etc. However, as mentioned above, no Antivirus package tested in the review was 100% successful at stopping infections.