How many GPUs can you simultaneously output from using a single PC?
I don't think there are any specific limits. Each GPU can probably drive three or four monitors, and with multiple GPUs in a system, I don't think there's any barrier to hooking up the maximum number of monitors to each GPU. Here's a video, for instance, detailing a 16-monitor machine with 4 GPUs, on Windows.

Googling around, I did find some people stating that Windows has a 16-monitor or 64-monitor overall limit, but I couldn't verify this from any official documentation. I also saw some claims that Windows has a limit on the overall desktop size that the monitors are virtually placed within, but again could not verify that. In Linux any such limits (if they exist) would naturally be different, and presumably would depend on which window system you're using.

The other potential limiting factor would be CPU performance and PCIe bus bandwidth for keeping all those GPUs fed with data.