CRJ-200 First Officer reported loss of Cabin Pressure Control during compliance with an MEL procedure for bleed swap during climb. The flight crew requested priority handling and descended to a lower altitude. The flight crew continued to destination airport with the packs in off position.

Narrative

Climbing out of ZZZ; after following the company procedure to swap bleeds during single pack operations at approximately 10;000 feet; we received a Right Pack High Press Caution Message climbing through approximately FL230. We started a precautionary descent since we then had no packs and soon would start to lose pressurization. We requested 10;000 feet and were assigned 11;000 feet. We started the APU below 15;000 feet and then once we felt we were at a safe altitude; started to run the appropriate checklist for the malfunction. Cruising at 11;000 feet we were unsuccessful at controlling the pressurization and then received the Cabin Altitude Warning; which then we officially requested priority handling and continued the descent to 8;000 feet. We ran the appropriate priority checklist and all applicable QRH (Quick Reference Handbook) checklists for packs off and continued to ZZZ1 and landed without further incident.The cause of the event is unknown. The MEL procedure has guidance for this event if it is associated with the bleed transfer. Since there was a long time gap between transferring the bleeds single pack and receiving the caution message; the cause may not be directly related to the single pack operating procedure. I believe events like this are unpredictable and cannot be fully avoided. My Captain and I used our resources and followed company procedure to handle the situation and were able to handle the situation to the best of our ability and landed without further complication.