You can book your business trip with AA if you want. That won't give you any leverage with UA. Wouldn't give you any leverage with any other airline, either.

The way it works (UA, and every other airline), each ticket is a contract with each passenger. You can split yourself off the record, and cancel the flights for the other travelers, however, the credit will be split between the other three, and each amount (after payment of the change fee, for each person) can be used only for another itinerary for the passenger named on the ticket (and travel must be complete within 1 year of the original issue date of the tickets).

There is only one way you can use the credit for other people. Cancel the tickets, and re-book each of the passengers on the cheapest route you can find. The difference between the original price and the new price (after you pay the change fee) will be issued as an electronic voucher, which can be used for anyone. However, only one electronic credit can be used for each person on a given itinerary - so if it is only you traveling, you can only use one electronic voucher.