Air carrier pilot reported a pressurization problem in cruise flight. The flight crew returned to departure airport.

Narrative

At approximately XA:50Z after we passed ZZZZZ on route to ZZZZZ1 at FL 330 and talking to ZZZ radio; we got four level 2 alerts: CARGO DOOR UPR A; CARGO DOOR CTR A; CARGO DOOR AFT A; CARGO DOOR FWD A. The QRH directed us to descend to 15;000 ft and to land at nearest suitable airport; so we [requested priority] and began our descent and turned around heading back towards ZZZ1. At approximately XA:03z at 15;000ft on about a 220 degrees heading and an indicated airspeed of 300kts we dumped fuel. We dumped fuel for approximately 5 minutes and 24;000 lbs; we started with 124;000 lbs and stopped the dump at 100;000 lbs of fuel. The remainder of the flight was uneventful; just operating the pressurization in manual per the QRH and landed Runway XR in ZZZ1. According to maintenance when we arrived back in ZZZ1 the issue was a malfunction with the miscellaneous systems controller. Is a malfunction of a component and these things happen; unable to prevent it just have to work with it and use good CRM to get the aircraft safely on the ground.