https://www.southwest.com/html/custo...and_conditions

Surprisingly the Rapid Reward terms do not specifically state something like "the Member must fly on all flights the companion flies on," but it seems pretty clear that is their intention.

It says this in the section on redeeming points:

"Member can use his or her points to purchase seats for him/herself or others; however, the Member is solely responsible for making any changes to the itinerary after booking. A Passenger traveling on a ticket using points from another Member's account will not be allowed to make changes to the itinerary. The Passenger must contact the Member and have the Member make any necessary changes."

I guess it is implied their that when the Member is using his or her points to purchase seats for others, the CP cannot be used.

For some reason they felt it necessary to spell this out in the CP terms: "An individual may not travel as both a Member and a Companion on the same flight." What does that mean? Would that involve bringing a cello with you?