Does the game crash if you leave it at the main menu, or are just in the options?
Have you tried other, similarly demanding DirectX 11 games recently? Crashes getting progressively worse can be a sign of hardware issues (or file corruption).
Are you shutting down all non-essential programs (especially anti-virus) before starting the game?
Try exiting out of the Galaxy, if applicable, and starting the game directly from the '..\Divinity - Original Sin Enhanced Edition\Shipping\EoCApp.exe' program file, by right clicking and running as administrator.
Did you try lowering the resolution when changing the graphics settings, or switching to Windowed or Fake Fullscreen display mode?
One person reported stability problems in D:OS if they had Ambient Occlusion enabled, for example, but the game was fine if they disabled it and enabled it in their graphics drivers. You could try disabling all the post processing in the graphics options, etc, if you didn't already.
Another was getting random reboots, which they tracked down to the graphics options in any game being different than was set as default in their video drivers (for anti-aliasing, ambient occlusion, etc).
Do you have Vsync enabled, or the frame rate cap set in the options? Try enabling, lowering or disabling those options.
Try lowering your desktop resolution, and limit the refresh rate to 60 (if it is higher), to see if that helps.
A program like DesktopOK
would let you save and restore desktop icon positions, in case lowering the resolution moves anything.
Try doing a clean boot and then test the game. Click Start, or hit WinKey-R, type in msconfig and hit enter; in the General tab, click Selective Startup, uncheck Load startup items (if required) and leave Load system services and Use original boot configuration options checked. Next, click on the Services tab, check the box to Hide all Microsoft services, then click the Disable All button (maybe make a note of which are currently enabled/disabled), then click OK and reboot the computer.
Run msconfig again to switch back to the normal boot configuration.
Try creating a new Windows administrator user account, switch to that account and try starting the game from there, directly from the executable to test.