I managed to upgrade a 2009 Mac Pro to High Sierra (10.13.6). According to Apple, it wasn't supposed to go that high but I found some instructions. Had to download a file to a USB and reboot. Sorry, can't remember details, but it can be done depending on machine.

If I replace a video card, I could bring it up to Mojave (10.14.6) and probably Catalina (10.15, next month) but not worth the expense.