Gulfstream IV Captain reported loss of both Air Data Computers on climbout; resulting in an altitude overshoot and subsequent air turn back for a precautionary landing.

Narrative

Takeoff roll above 80 kts. just below V1 (122) received CPL DATA INVALID; DADC MISCOMPARE; MACH TRIM OFF; STALL BARR 1 FL; ICE DETECTED; YAW DAMPER OFF. Takeoff was continued as briefed. After takeoff received alternating ADC1 and ADC 2 failures during climbout. Stick shaker activated on both sides wIth AOA at 1.0 (RED) on both pilot and copilot sides during takeoff and initial climb. Auto throttles and Flight guidance were unavailable. PF (Pilot Flying) continued flight using known pitch and power settings during climb assigned by ATC; while PNF (Pilot Not Flying) was running QRH checklist. Clearance was to climb to 6000 feet. PF showed 5000 feet and climbing on Altimeter; PNF altimeter showed 6500 climbing when ATC notified crew the clearance altitude was 6000 and was showing primary radar at 7500. PF immediately took corrective action and radioed ATC of failure of both flight computers (ADCs) and began using standby instruments to return to 6000. Crew elected to return to ZZZ for ILS XX approach given by Approach Control. PNF ran QRH checklist items and standard normal procedures checklist items. Landing uneventful. Altitude deviation was due to both Air Data Computers failing and crew saturation with checklists and multiple failures in connection with ADC during climb. PF believed the data presented on Primary Flight Display number 1 to be accurate during initial climb out; however at some point recognized both ADCs had failed during the climb to 6000 ft. PF was unaware ADC1 failed until ATC notified crew of altitude deviation via radio and confirmed this with ADC1 failure message on PFD 1. A faster transition to standby instruments by the PF may have caught the deviation developing sooner.