A321 Captain reported a fume event during preflight. After extensive maintenance action with no remedy; the flight was cancelled and ferried to a maintenance base the following day.

Narrative

Aircraft X experienced a reported fumes event after start of engine #2 at the gate in ZZZZ. Aircraft Y arrived from ZZZ - ZZZZ; having just experienced a fumes event in flight. The inbound Captain placed the write-up in the logbook; completed the Fumes Event worksheet; and debriefed Maintenance. In coordination with Maintenance Control; ZZZZ Maintenance personnel performed the required procedure to troubleshoot the source of the fumes. I coordinated with Company; and Maintenance personnel; and went up to the gate area to inform the customers of the situation. Over the next hour and a half the First Officer and myself assisted the ZZZZ Maintenance personnel to complete the lengthy procedures. The customers and personnel were given periodic updates by myself; while the flight attendants remained in the discussion throughout the process.Coordination and operational updates between myself and the Chief Pilot continued via cellphone throughout the night. It was determined that the likely source of the original fumes event was the APU. Subsequently the Bleed Air portion of the APU was MEL'ed and the aircraft was placed back in service. Customers and crew were briefed and boarding was initiated. At this point; due to CBP (Customs and Border Patrol) limitations; we needed to depart within an hour; which included a 20-minute coordinated extension. Engine #2 was started at the gate due to the APU Bleed Air not being available. After the engine was started; before pushback was commenced; I received an interphone call from the F2 stating the odor/fumes were once again prevalent in the area of Row 23 and that customers were also complaining about the fumes. The FO (First Officer) and myself did not smell any fumes out of the ordinary.The engine was shut down; the jetway was brought back to the aircraft; and the boarding door was opened. Since we were now going to be past our 'latest departure time' due to CBP restrictions; it was decided to deplane the customers as we started working with Maintenance on the fumes event. No customer health related issues were noted due to the fumes; to my knowledge. The flight was subsequently cancelled by Operations. The flight attendants were released to a hotel as a new flight segment for the customers was built for the next day… a new plane would be flown in. The customers were briefed about the situation and remained in the boarding area for a time as accommodations were coordinated.The FO and myself remained with the aircraft to continue work with Maintenance. The plan; as coordinated through the Chief Pilot with Operations; was to eventually ferry the aircraft out of ZZZ to a maintenance base; if the aircraft could be placed back in service. After subsequent review; Maintenance Control; Operations; and both the FO and myself all agreed that MEL'ing Air Conditioning Pack #2; along with the already MEL'ed APU Bleed Air; would be sufficient… the aircraft would then be a ferry flight to ZZZ1; as it was the only maintenance base available due to CBP restrictions in the other bases. The length of the maintenance procedure for securing Air Conditioning #2 Pack per the MEL meant we would be close to the airport closing time; at which point we would not be allowed to depart. Coordination was initiated to request the airport closing time be extended for our situation. In the end; just as the maintenance procedure was completed along with the subsequent logbook paperwork; airport Tower reported the airport was closed. It turns out our request to extend the airport closing time was denied but never passed on to us.After further coordination with Operations; the ferry flight was cancelled and rescheduled for the next morning. The FO and I were released to rest. The Company coordinated to have ZZZZ Immigration come back to the airport and clear the FO and myself back into the country. He also coordinated with our normal driver for airport pickup; as we awaited a hotel assignment. The next day morning; the FO and myself returned to the airport and completed a ferry flight of aircraft to ZZZ2. The flight was uneventful with no fumes/odors noted.