[18.04] Is it possible to run two MATE sessions on two X screens in parallel?

As I already wrote here, I have trouble using LibreOffice with the Nouveau driver (default for Nvidia card) - it locks up my computer. On the other hand, I can run LibreOffice without problems on non-accelerated X server (with Nouveau disabled), but video performance is unacceptably slow in that setup.
So I have an idea to run two separate X servers (one with Nouveau and one without) and two parallel MATE sesssions on them, to run LibreOffice on the X server without Nouveau and everything else on the screen with Nouveau. Is it possible to do this? How?