Did lowering the graphics settings seem to make any difference to the frequency of the crashes? Did you try switching to Windowed or Fake Fullscreen display mode, to see if that would make a difference?
Try exiting out of the Steam client, and starting the game directly from the '..\SteamApps\common\Divinity Original Sin Enhanced Edition\Shipping\EoCApp.exe' program file, by right clicking and running as administrator.
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.
If there are any 'CrashDump' files being created in the '..\Divinity Original Sin Enhanced Edition\Shipping' folder, please zip a few together and email supportdos@larian.com (or email/post/PM a Dropbox or Google drive link, etc).