I think you are looking at 2 different things
Trying to retain India as part of a British Empire
Trying to make the UK a power to match the USA
For all the reasons people have said, there is no way to realistically retain India as part of a british empire in the modern world, the distance, the british idea of racial superiority, the fact that India was used to improve the economy of Britain, the demographics of India v Britain and the effect of democracy on any institutions etc
As for making Britain a power to match the USA ( and the USA as it is right now) is difficult, the USA is huge geographically with room to grow, from a post war population of 130 million to 300 million today.
The UK is unlikely to retain even canada, australia or new zealand as part of a british empire, the distances are too far for massive integrated trade and travel in an pre 20 century world, even in 20th century world. I mean Canada alone had dream of matching the USA with a 100 million population dream that never happened, so they would definitely want to leave.
One option would be if the UK pursued its 80s economic revival whilst not being in the EU, but using these links to improve trade within the commonwealth, as part of a beefed up commonwealth, especially among the white colony nations - canada, australia & new zealand and pursue combined research programmes, defence spending and beneficial trade agreements.
Also the UK could try to retain some of the smaller or weaker non white colonies or allow them to stay as part of the UK if they want (or buy them to stay with large subsidies - whilst promoting integration with UK). Malta almost stayed with UK, allowing smaller colonies within the west indies such as jamaica, belize or Guyana etc to stay within the UK and investing in them, might have worked. The populations aren't huge so the fear of vast amounts of non white immigrants isn't credible (although given british racial attitudes, even small numbers of immigrants weren't acceptable post war)
All these things are post war acts, not pre 1900 though
The point of retaining these countries would to be try and grow them economically and population wise on the grounds that a multi national UK of 60 - 70 million by the mid 1960s would be more independent of the USA, would be able to afford its own defence etc.
However the underlying weakness of the British economy and its post war decline might mean thats all impossible.
The other option is to retain Ireland, which would be a longshot, given hundreds of years of english abuse of the country and its people and would need an Ireland where the famine didn't happen, so the population didn't collapse. Again given british attitudes I am not sure thats possible.
Would Britain accept large scale immigration into the UK in the 19th Century? Could it grow its own population? it would never match the USA, but perhaps could be first among equals in Europe, with a population to match Germany, that might also mean it could stop the ww1 which broke the british empire financially. Due to racial attitudes, poor white immigrants are probably more acceptable, from spain, italy, eastern europe etc. A larger population might mean the other countries of the british empire might want to stay in its orbit and influence more easily
I haven't really discussed the non white african and asian colonies, as I can't see them wanting to stay in a british empire and given the poor success of the french in buying influence in the former french empire african countries, I am not convinced the UK could do any better without a more radical attitude and plan. again that would require lots of money spent over a much longer term
If you want to go much more ASB, england would need to retain parts of france, which become part of the UK, basically, Brittany, Normandy and Hauts de France ( region east of normandy). becoming part of the UK and becoming anglicised and crucially develop as part of the british empire, which grew faster than france. That adds about 13 million people to the UK today.
So basically my view is that if you grow the population of the UK that will make the UK stronger. 80 million makes it dominant in europe, 100 million makes it the european superpower and so on. But given the food needs of the UK, after about 60 million based on food production in the 20th century, it will need to have more farm producing land.
