NASA has bought six Crew Dragon flights and there is at least one private flight booked for next year. There are currently two flight-capable Crew Dragon spacecraft. Is SpaceX currently building more capsules and if so, how many?
Short answer: Three cargo and five crew vehicles.
Gwynne Shotwell answered this
Specifically, Shotwell revealed that SpaceX intends to build three reusable Cargo Dragon 2 capsules, one of which is already completed and in Florida preparing for its December 2nd CRS-21 launch debut. On the crew side of things, SpaceX will build “three more” Crew Dragon capsules on top of the flight-proven Demo-2 and currently orbital Crew-1 capsules. It’s unclear if this means that the new Crew Dragon capsule flown on SpaceX’s January 2020 In-Flight Abort (IFA) test will be refurbished for additional flights.
Excluding IFA Crew Dragon capsule C205, SpaceX thus intends to operate a fleet of at least three Cargo Dragon 2 and five Crew Dragon capsules, representing eight reusable spacecraft each capable of at least five orbital missions.