United already has code sharing agreements for daily flights into multiple cities in Pakistan via Doha on Qatar Airways. Why would they care to connect to PIA’s 2 weekly flights?
The only way I could see that being worthwhile is if PIA establishes a European hub with daily nonstop service to Karachi and Lahore (and possibly less frequent nonstop flights to secondary cities like Islamabad and Faisalabad), and codeshare on AA/UA feeder flights from across the US to the European hub.
As it stands, with 2-3x weekly flights to a string of Pakistani destinations, there’s really no reason to chose PIA over any of the Middle Eastern carriers.