You can do Brotherhood quests right up until "Tactical Thinking," which requires you to destroy the Railroad (immediately thereafter you're tasked to destroy the Institute).

You can do Railroad quests right up until "Precipice of War," which requires you to destroy the Brotherhood (immediately thereafter you're tasked to destroy the Institute).

You can do Institute quests right up until "Mass Fusion," which turns you hostile to the Brotherhood (thereafter you're tasked to destroy the Railroad, and subsequently also the Brotherhood unless you destroyed them with the Railroad already).

The only thing to watch out for is the beginning of Mass Fusion. You want to avoid the first objective, "Talk to Allie," until you've reached the cutoff point with the Brotherhood, because once you do talk to Allie all dialogue with the Brotherhood officials gets locked into a Mass Fusion turncoat ("Hey, the Institute's about to start fighting you, we should hit them first.")

The cutoff points are also really obvious, you'll be notified explicitly when you've reached them, either you'll get a popup message saying "If you proceed you'll be hostile with X faction forever" OR in one case it'll just make you hostile right away but you simply reload your latest save.