Since, despite the severe setbacks of 2 world wars and the depression, the white Dominions saw themselves as part of an Empire and Commonwealth until at least the 70s I don't think it would be too hard to have the Empire last longer. The first thing in my mind is to do better in WW2, there are thousands of ways to do this, they are the common fodder of this board. This will give Britain and the Empire greater intertia. A second thing would not to join the EU, or perhaps later than OTL, so trade within the Commonwealth was stronger and of greater value. Thirdly would be perhaps introducing a British Commonwealth version of the dual key nuclear arrangment that NATO had with the US, this would bind the Commonwealth together as a group of nuke holders.