Fake Secondary Xorg Server

Would it be possible to make a second fake xorg server such that:

• There is no real physical monitor that it connects to, but the GPU can still do the calculations to render to a fake or "dummy" monitor?
• I can still use another xorg server to display use my actual physical monitors normally
• I can take a screenshot from the fake secondary server and get the picture that would be rendered to a monitor if there was a real monitor being rendered to?
• I can use a NVIDIA graphics card to drive this secondary fake xorg server and the normal one simultaneously?

If so, how would I go about doing this monitorless, simulated graphics environment? I currently most often use GNU/Linux, but I would be open to doing it on Windows, BSD as well if GNU/Linux is not possible.