There isn't a single mainstream OS that supports having multiple mouse cursors that I know of, and even if it did, not a single program expects it either - most would break. The closest we have is on-line editors that can have multiple users like Google Docs, and that's not single screen.
And you may be thinking "yeah but why?" and I wouldn't blame you, but that's just because you're not aware of how how much our current input devices limit us and how they are based on a flawed model of handedness.
Yves Guiard proposed a model in 1988 that argues the dominant/recessive model of handedness is wrong: instead, we constantly perform complicated asymmetrical tasks, with one "coarse" reference-frame hand and a fine-tuned "zoomed-in" hand (the latter being considered the dominant one)[0]. Later research has only backed this up (note that the linked paper has over a thousand citations).
When keeping this asymmetrical model in mind designing our input, things tend to just "feel" right. I guarantee you that the best two-handed input methods you use all follow this principle: even if not applied consciously, any two-handed interfaces converges to it. Simple case-in-point: remember 3D shooters before WASD + mouse? WASD = reference frame hand, mouse = fine-tuned input hand. Gamers just intuitively discovered this on their own. In fact, look at button placement on gamepads in general: movement ("frame of reference") on the left, action buttons on the right.
Bill Buxton[1][2][3] did really cool experiments with these ideas and then... well, nearly nothing. And I really believe the main reason is a lack of technical freedom to experiment: even if someone does manage come up with a wonderful intuitive, fluid bimanual interface that isn't limited to a keyboard, a mouse and maybe a touch-screen, who is going to be able to use it on their laptops or desktops?
I'd like to experiment and the fundamental requirements to do even that are missing. Even multi-touch is barely going to help: you cannot tell which hand belongs to which touch-point.
[0] https://www.ncbi.nlm.nih.gov/pubmed/15136274
[1] https://www.billbuxton.com/2hands.html, video: https://www.youtube.com/watch?v=w0c1Xg9lERY