It would not be a matter of allowing India to dominate.
I can imagine the following scenario.
An India united under the Raj will quickly be more powerful and stable than OTL, and only slightly slower will they develop independence. I have read that at one point, only a thousand British ex-pats were running the whole show over there, the rest of the civil service was Indian or Indian born Brits. I can believe this. India will be more stable, which is to say, more uniformly unstable. The instability will be focussed on anti-British feeling, in the way that anti-Pakistani feeling was a stabilizing force in our timeline. If it is played right by the British, it will never boil over. So by the 50's, India is under the nuclear umbrella of Great Britain, and will likely never fight a war on the scale of the wars with Pakistan or China. To maintain peace, the Raj gradually becomes more Indian and less British.
The rest of the Empire federates, with Great Britain being the leader, the Dominions, the settler colonies that is, just below, the Raj outside this system, and the other colonies ruled directly from London. At first, the trick will appear to be, how to balance the economic, military and political power of the Dominions with that of Great Britain. And so maybe Britain will keep a veto, and this might be the case for decades. But by the 80s, it will be obvious to outsiders that the Raj is the economic power, though not the military or political one. And the Dominions and Great Britain will put their differences aside, and just about balance their power within the Empire. I can imagine the other colonies gain independence five or ten years behind schedule. The Dominions do not gain independence, since they are in more of an EU type situation.
The Raj will be in a strange position, though. It will not be a democracy, though it may well be a meritocracy, through the civil service exams, and it is definitely a capitalist system. Whoever is in charge will make a decision to remain in the Empire, and enjoy the benefits of doing so, in terms of trade and defence.