My old shop vac didn't follow me well any longer and it tipped over very frequently when it "tripped" over the cord or any little grain of dust on the floor that happened to be in the travel path.  These events consistently made me very unhappy and I finally decided to do something about it.

I had a broken furniture dolly that had the long members broken at one end.  I removed the broken pieces and shortened them so the vacuum body would rest on the higher cross pieces.   Once the dolly was reassembled, I put the vacuum canister (body) on the dolly so it overlapped the higher area of the dolly on each side, then put a drywall screw through the bottom of the vacuum body into the dolly on each side. 

The larger casters and larger base allows it to travel much better and more easily, even going over its own cord, and it has followed me around the shop without incident - no tipping or stopping - in the 3 weeks of use since I've done the mod.