Would that even be possible? SpaceX would need to either provide intense training (engineering, operating, etc) for their rockets, or to provide the staff and facilities themselves; basically the company would need to double its staff (if not more) to support a scheme like that.

I mean it makes sense, why not sell off rockets and whatnot commercially like the mass production strategy that Musk has in mind? But I don't think there's enough launches yet to warrant that. In fact, SpaceX is booked full for the next few years already; unless that's intentional, they simply don't have the production capacity to humour that idea.