If the Brotherhood of Steel changed their way of thinking, then they would lose their identity as a faction. Where they are now is as a result (and a reaction) of multiple chained events within the faction's history which would be difficult to change without a very important reason to do so.
Just looking at Arthur Maxson's BoS chapter, you can see traces wherein the faction has kept, adopted or discarded bits of their philosophy or behaviour as a result of their unique history. One need only compare Lyons' Brotherhood in 2277 to that of Maxson's in 2287 and ask what happened to them in that time, and more importantly, what happened to Maxson, to see how events ultimately changed them and their ethos.
It is a distinct possibility with the Brotherhood that a chapter could emerge with a different line of thinking which might suit your interests more, however that would not define the whole Brotherhood.
To a large extent, chapters operate with autonomy, and so long as they do not deviate from the Western Brotherhood's (Lost Hills) style of thinking too drastically, their identities and interpretations of Brotherhood belief can vary widely. It would take a serious event (most likely located at Lost Hills) for the highest echelons of Brotherhood society to change their ideology and philosophy, and even then, there is no guarantee that geographically estranged chapters will accept them.
The Outcasts were a faction of their own that split (adopting their identity) for very specific reasons concerning Elder Lyons' leadership as of 2277. A separatist faction could spring up within the Brotherhood again, but it wouldn't be the Outcasts as we know them. At most they may be "Outcast-esque" in their attitudes or perhaps even appearance (as Brotherhood separatists would make use of robots more to compensate for their small numbers, and make themselves distinct from who they were separating from, as the Outcasts had done).