And what about the details?
Lemme try, then:
1) Have Brazil have its OTL 21st century borders (so Brazil does gain Acre, but no glorious Brazilian Empire that stretches from the Amazon to the Andes, the Atlantic to the Pacific.
Pretty easy, the 21st century borders are mostly the result of long diplomatic issues. After the Paraguayan War, Brazil has mostly modern borders.
2) Try to have more Protestant immigration. While I'm definitely not saying that Brazil needs more Protestants to be more successful, I do believe that a more stable Brazil could have attracted more Protestant immigration than OTL, especially from places such as Scandinavia, Britain and the Low Countries. Anyway to make Brazil 15% Mainstream Protestant (so not any Pentecostal movement but instead traditional Lutheran, Calvinist and Anglican Protestantism).
A weird requirement, and I say this as a Protestant.
Brazil already attracted a lot of protestants. In fact, the first real protestant communities started in immigrants from Germany, if I remember right.
I'm not sure anything else can attract even more protestants, aside from better economics, which are practically a given if the Empire continues. The thing is, the United States is far more attractive to Protestants - its richer, its more tolerant and is a protestant country. Back when, and heck, even today, Protestantism in Europe is kind of a "Northern European" thing, Mediterranean Europe is strongly catholic.
Also the climate is definitively not friendly to Northern European types. There's a reason the main european stock in the country is Mediterranean. They could go to Southern Brazil, sure, but that's frontierland.
3) Elaborate relations with its neighbors, various European powers and the U.S.
Brazil has pretty elaborate relations already.
Now, the thing is, until recently, we were never too much buddy-buddy with our neighbors. They were a bunch of strange people spanish-speaking and spent almost a century picking fights with us. A stronger, more prosperous Brazilian Empire might have a good effect on the continental economy, especially if it keeps liberal economic policies. If Brazil industrializes, it will seek these countries as potential markets, and these countries will try to block brazilian goods in order to industrialize themselves. I suspect some countries like Argentina and Chile will industrialize and block, while Uruguay and Paraguay, possibly Venezuela as well, might fall under Brazil's influence.
I rather doubt that we will see Brazil in any big alliances or the like. That's not how Brazilian Diplomacy ever worked, Brazil in the international scenario is "That Guy Everybody Likes".
The Empire will have dynastic ties with the house of Habsburg, which might mean Brazil is closer to the Austro-Hungarians. This might be relevant in the future.
I don't think the Empire will want to involve itself in any world war. These will also lead to a "Import Substitution" model, if only to prevent the flow of industrialized goods from stopping every time someone starts doing naval fighting in Europe.
4) Elaborate Brazil's long-term economic condition in this ATL.
Without the mess that is the Old Republic, I would say Brazil is AT LEAST 10-40 years richer than OTL. This might be enough of a difference to catapult Brazil into what we call developed status, or close.
And what about the details? Could we see more British Brazillians than in OTL?
Not probable. They got better places to go - the US, Canada, Australia, African colonies... being a British colonists at the time meant a lot of choice. Far easier for them to go places full of other white anglo protestants.