Philadelphia built and owns the Broad Street Subway, which is why the trains bear both the SEPTA logo and city seal. SEPTA leases and operates it from the city. I don't know the terms of the agreements that arrangement, but I suppose that the city could theoretically retake control and operation of the system as well as any extensions thereto. It would presumably be bureaucratically complicated. The city would need to establish a relationship with FTA to receive formula grant funding, establish a bureaucracy to operate and maintain the system and mercy knows what else.

It might be worth noting that even when the city envisioned building a system of municipal lines, it never really expected to operate them. Many of the old reports of the Commissioner of City Transit deal at length with establishing the legality and negotiating the terms of an agreement with the Philadelphia Rapid Transit Company to operate the lines built by the city. Indeed, when the Broad Street Subway at last entered service, the PRT, then its success the Philadelphia Transportation Company, operated the service.

Even if Philadelphia were to do this, they would still need to cooperate with SEPTA, because of the Broad Street Subway's transfer points with the Market-Frankford Subway-Elevated. Assigning operations to PATCO is an amusing proposition, but I doubt that the Port Authority would want to assume control of a line that is entirely in Pennsylvania. (N.b. The city also built the 8th-Locust subway, originally as part of a never-built line that would have crossed the river and run over Woodland Avenue to the city line; PATCO uses that segment under lease.)