I like to think that they're the bad guys of the BOS, and are interested in expansion where the others want to sit tight.
The Midwestern BoS would honestly make for a great villainous faction (as they were intended to be, after all). They're ruthless militant expansionists who, having learned from their predecessor's mistakes, now not only welcome others into the fold but depending on your ending they will force them to.
Also depending on your ending they may or may not put mutants in camps and they may or may not possess the greatest manufacturing facility and weapons arsenal in the US, as well as a sentient supercomputer powered by a council of human brains and an army of machines.
But what is really interesting to me is that the Midwestern BoS don't simply engage in military strategy and combat, like the Californian Brotherhood did or even the DC chapter. No, they have their own CIA: the Inquisitors, sadistic interrogators and agents that act as the Midwestern BoS's personal Gestapo, as well as regular police force and spies.
Considering that by the end of Tactics their territories reach from Chicago all the way to the Cheyenne mountain complex, if the ending permits it wouldn't be far-fetched to assume that they've sent agents into the Legion, the NCR and beyond and nobody is any the wiser.
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A lot of their presumed potential is based on the assumption that one of two specific endings has happened: a member of the player's team has sacrificed themselves with either good karma or bad karma.
I think it's probably the latter.
In the first one, the Midwestern BoS basically stamp out racism forever, create fair laws and usher in a post-apocalyptic utopia within their borders. The wealth of technology afforded to them by Vault 0 is used to help their civilians and other such nonsense; it's your stock "best possible outcome" ending.
The second has the Calculator become truly complete for the very first time; it allies itself with the Midwestern BoS, but chooses not to officially join its ranks. Eventually, it secretly murders all of its Elders and takes direct control, ushering in an age where efficiency is seen as their top priority. Racism is made illegal not so much because it's wrong, but because mutants are valuable resources; by the time we leave the Calculator, it is considering the best possible way to approach its inevitable contact with the original Brotherhood.
The remaining two endings have the Midwestern Brotherhood fight either the Mutant Liberation Front in response to their camps or various civilian uprisings and rebellious factions following their weakening. Either way, they lose a lot of territories.
Caesar's comment tells us that the Midwestern BoS still has a foothold as far West as Colorado, excluding General Barnacky's ending and the destruction of the Calculator; after that, it becomes more speculative.
Fallout 3 tells us that the Chicago chapter has not only established a recruitment policy but that even mutants are allowed, which is something that occurs in either ending. They also mention them having come into some trouble last they've heard, but that doesn't tell us much; it could be referring to the assassination of their elders, but that was years ago and it seems unlikely.
However, the DC BoS also tells us that the Chicago chapter has refused Lost Hills' authority and is, at best, a reluctant ally to the original Brotherhood. They also mention them 'falling off the radar', meaning that they are no longer reporting in.
Though it's not conclusive proof, the 'Good' ending to Tactics has the Midwestern BoS prepare for a diplomatic meeting and shows them to be willing to work with the Californian BoS, while the 'Bad' ending tells us that the Calculator is wary of them and is not going out of its way to contact them.
Though it is entirely possible that diplomatic relations simply fell apart, it seems more likely that the Calculator simply cut off contact; after all, it has a precedent for refusing to accept the Brotherhood's authority in favour of simply remaining their ally and if history is anything to go by, it's probably planning their destruction.
TL;DR the Midwestern BoS would make cool villains and the canon ending is probably the poor karma "player squadmate becomes the Calculator" one
