A320 Captain reported being notified by the Flight Attendants of an 'intense fume event' in the cabin. The Flight Crew returned to the departure airport.

Narrative

Shortly after takeoff; the inflight crew notified me of an 'intense fume event' that was happening in the back half of the cabin. I was told that passengers were very much complaining and trying to move to the forward half of the plane during the climb-out; approximately 4;000 ft. The inflight crew had to relocate as well.We immediately ran all necessary procedures. I asked my FO (First Officer) to continue flying and to take the radios so that I could begin troubleshooting. The odor isolation procedure proved to be unsuccessful. After each step; I checked back with the inflight crew to see if conditions improved. They did not. The QRH procedures were also unsuccessful; up to the point where we were forced to turn BOTH packs off. At this point; it was obvious that we would not be able to climb above 10;000 ft. due to our unpressurized state. Continuing to ZZZZ was no longer viable. At this point; I assumed the radios and asked ATC for a return to ZZZ.Inflight crewmembers stated that the fumes had subsided at this point; but they were experiencing symptoms such as dizziness; burning eyes; chest pain; and labored breathing. Each inflight crewmember seemed to have different symptoms. I asked if they wanted medical attention; to which they declined. As we got closer to ZZZ; I told the First Officer that I would rather request help and not need it rather than the other way around. While the First Officer was managing the aircraft and radios; I notified Dispatch; ran the divert QRH; the Over-Weight Landing QRH; helped reprogram the FMS; etc. A normal approach and soft landing was made. All overweight considerations were made and the emergency vehicles followed us to the gate. No assistance was needed. Upon arrival; a normal deplaning was conducted. EMS checked out the entire crew.