At present, one credit card may be used per reservation, not three. Here's the policy:
A maximum of three forms of payment per Passenger may be used to purchase an itinerary. The following may be used per Passenger: up to three flight credits, up to three Southwest gift cards, and/or up to two Southwest LUV Vouchers®.
When booking a reservation online, flight credits will always be applied first, regardless of the order in which a Customer enters them in the reservation.
The following may be used per Passenger: up to three flight credits, up to three Southwest gift cards, up to two Southwest LUV Vouchers®, and/or a credit card (only one credit card may be used per reservation).
https://www.southwest.com/help/booking/forms-of-payment
I have not seen nor heard of any plan or proposal to permit up to three credit card payments per air fare transaction. A possible workaround would likely be to book two separate cheaper flights with the second and third credit cards but cancel these and use the flight credits plus the first credit card toward the purchase of the real flight.
