Bracketing exposures and flash at the same time?

[LongLensPhotography]

Let's say I want to bracket exposure EV -3.0 and flash -2.0; 0.0 and 0.0; +3.0 and +2.0 or something similar along the lines. I can do this manually but wonder if there is a way to do this automatically?

I use Canon 5d mk3. Whenever I switch on the flash trigger it cancels bracketing.

This should hopefully save a lot of photoshop blending for some images.