Is it possible to file a lawsuit against aaa roadside regarding the car damage my vehicle received from their contracted towing services?

A towing service provided by aaa road side service repeatedly damaged my vehicle. After notifying aaa about the damage they explained that liability insurance does not protect the driver's vehicle. My vehicle received severe damage during a towing process when a tow truck mishandled it. The branch manager directed me to find cost estimates yet refused to accept accountability during this three-month period while work stopped and my professional truck suffered major damage.