A patient transport apparatus transports a patient over a surface. The patient transport apparatus comprises a base and support wheels coupled to the base. An auxiliary wheel assembly is coupled to the base and comprises one or more auxiliary wheels that influence motion of the patient transport apparatus over the surface to assist caregivers. An actuator system is operatively coupled to the auxiliary wheels to move the auxiliary wheels relative to the base from a stowed position to a first deployed position, and further to a second deployed position.