I really wished this was an option, basically go to Maxson, Desdemona and Father and persuade them to attend a meeting, probably in Sanctuary as that would be most fitting.
I think the BoS and the Institute would be easiest to reconcile, though I would expect discontinuation of Gen 3s to be one of the conditions. Gen 1s and 2s maybe allowable because they're at least identifable as robots and are more on the same level as Protectrons, Mr Handys etc. But I think convincing that them that the BoS can be the brawn and the Institute the brains of a joint venture is doable. Together they would certainly be a potent force, the Institute are surely able to provide tech that could be used to upgrade the BoS' power armour, weapons and airfleet.
The Railroad would be more problematic but they have good intentions, could they become the heart of the new order? Perhaps as a kind of ethics committee on AI? It would be a hard sell to all sides for sure but I think a place could be found for the Railroad in such an alliance under the right circumstances.
This leaves the Minutemen, who would pretty much accept BoS and Railroad, again a hard sell when it comes to the Institute but I think the Minutemen would be the most likely faction to be open to an alliance. In this case I would expect them to become a kind of police force of the Commonwealth, calling in the army - the BoS - when necessary.