Probably needs a 19th century POD (so pre-1900) and would need actual widespread interest both in the UK and overseas (of which, in the UK's case, there definitely was
not outside of Joseph Chamberlain's circle). Otherwise:
If the POD is far enough back that Canada and Newfoundland (still a separate Dominion at this time) are included, there's already a major problem lodged within the system, even more so than Ireland. It's Québec, or rather the whole of French Canada (of which in Québec it's in the majority). As French-Canadian nationalism matures, its people are going to find the Imperial Federation arrangement unsatisfactory since it's just colonialism by another name. Therefore, it's going to want independence, if not for all of Canada than just Québec and maybe some adjacent areas of Ontario and New Brunswick. Then the Imperial Federation starts to become unworkable with the departure of Canada, even in part.
"Superpowers" really don't exist outside of a Cold War-era conquest just for the US and the USSR. If similar entities existed at all, the preferred term during the period was "Great Power". Much less attractive, but still gets the point across.
And that's going to be another thorn in the Imperial Federation's side, outside of French Canada. Given the Second British Empire existed primarily to serve India, Indian politicians will demand it be included inside the Imperial Federation. If it's excluded, it's going to demand independence - which means the Empire will go and the Imperial Federation will start to develop cracks.
Of those two, even if the POD is far back enough, the Caribbean would much more likely than any of the African colonies. The vast majority of them would prefer independence, even Sierra Leone. However, having said that, if you really wanted to throw a left-field curveball on that - if the Caribbean is being retained, and if Britain still holds the Chagos Islands (now known as the BIOT), then it could be possible to retain Mauritius and the Seychelles, both of which are very diverse communities and which could be seen as the Indian Ocean's version of the Caribbean.
Natal is a no because it would involve South Africa, which was never really all that interested in the British in the first place. So South Africa would have to be coaxed in somehow into the Imperial Federation, which means London would be ultimately responsible for apartheid (even if it was stuck in its pre-1948 forms) whether or not it consented to it. As for Rhodesia - which one? Northern or Southern? Though even in the latter case, a secessionist regime would not work if the majority of the population prefer independence over Imperial Federation, regardless of the wishes of the rulers.
Singapore is a no - until independence, it was primarily an economic backwater whose only good fortune was its location. Otherwise, its leaders preferred joining what would eventually be Malaysia, no matter what, alongside fellow Straits Settlements Penang and Malacca. As I see it, the main way Singapore gets involved is if the other 2 Straits Settlements are included (the minor Strait Settlement at
Dinding excepted), since even as far back as the early 20th century it would be hard to tell then what Singapore would become now.
Similar problems bedevil Aden and South Yemen. In this case, not only would the sheikhs and all that in the hinterland be consulted, but I would make the bold claim that holding onto Mauritius and Seychelles, not to mention keeping the Trucial States (except Oman - despite all appearances, it kept its independence all throughout this time), would be necessary for the security of South Yemen. Even then, pan-Arab sentiment means that Britain's holdings in the Middle East would eventually be on shakier ground. Something would have to give that would lead into demands that Britain withdraw from South Yemen and the Trucial States.
TL;DR - From my perspective, the Imperial Federation was unworkable even in theory, due to multiple factors both domestically and abroad. Once specific territories are named, then it becomes a problem where the risks outweigh the benefits, with especial problem areas being Canada (particularly French Canada) and India.
