I’m not sure yet which of two flights I want – is it possible to hold both?

Unfortunately, no. Holding more than one reservation is considered an illegal practice by the airlines which can lead them to cancel all of the reservations without notice and send the travel agency debit memos for illegal booking practices. In recent years the airlines have employed increasingly sophisticated technology to identify and cancel multiple reservations that cannot possibly be used by the same person. This includes not only reservations containing some or all of the same flights, but also those that contain different flights operating in the same general area and time frame (i.e. one reservation on May 15 Reagan National to Chicago O’Hare with a return on May 18 and another reservation on May 15 Dulles to Chicago O’Hare with a return on May 17).