My guess is you can use however many UA Clubs you can access during your trip.
https://www.united.com/ual/en/us/fly.../packages.html- United Club℠ trip pass: A United Club trip pass grants a traveler access to all available United Club locations, not including United Arrivals Lounges, United Global First℠ Lounges and United Polaris® lounges. You can use the pass at the departing, connecting and arriving airports for one direction of travel, although some lounges may not be accessible after landing on international itineraries. The pass is only good for the person named on the boarding pass (no guests) and expires upon completion of the trip.