mudpuppet :
Technically, you could, but I guess the question would be why? The first GPU should have enough ports (usually at least 3) to run 2-3 monitors off of.
When I was working on a flight simulator project for the USAF to replace $6 million Silicon Graphics hardware, we hooked up something like a couple dozen graphics cards to a single PC using PCI extender boxes (PCIe hadn't been invented yet).
Commercial airliner simulators are mostly limited to the horizontal axis (relative to the cockpit), so they get by using mirrors to project a narrow but wide image. The USAF simulators were combat simulators so stuff above, below, and behind you mattered. So they used interlocking flat hexagonal screens looking kinda like the inside of a giant insect eye. (From the link, it looks like the newer ones use pentagon screens.)
http://www.airforce-technology.com/contractors/training/link/
Each screen was driven by a separate graphics cards (in SLI). The cards all needed to be in the same PC because apparently the framerate and refresh for every screen has to be synchronized. A slight lag between updates on adjacent screens was distracting.
So anyway, that's one use case where you might want to run a dozen or so monitors from a single computer.