A320 flight crew experienced three unrelated systems failures after takeoff and elected to return to the departure airport.

Narrative

Engine EGT over temp; recovered in idle; SE ILS return to field. On departure out of ZZZ at around 23;000 feet; we got a Brakes Hot ECAM. The temp on the right main gear inboard brake showed 400 degrees. The First Officer was the Pilot Flying. I coordinated with ATC to level off and we started slowing down so that we could drop the gear per the ECAM. As we were slowing down; the First Officer told me to take the airplane as she had just lost both of her screens. She selected the Autopilot to AP1 as I verbally told her I was now Pilot Flying. There was no initial ECAM associated with her display losses. Her screens came back but she informed me that her speed tape was missing and information was incomplete and not reliable. The ride was deteriorating rapidly at 23;000 feet with moderate turbulence and a fire. Our radios had a lot of static and communications with ATC was difficult; so we asked for a change in altitude. The Brake Temperature went down for a few seconds to 200 degrees making that ECAM go away but then it came back just as quickly. As I was still above 240 knots trying to slow down and maybe try a different altitude we got an ENG 1 EGT OVER LIMIT ECAM. We noticed the EGT high (at least 650 degrees) with the red tick showing. Our to do step said: THRUST LEVER (affected) - BELOW LIMIT. Retarding the number one thrust lever to idle brought the EGT back in the green.We requested priority handling and asked for immediate vectors back to ZZZ. The Brakes Hot ECAM meanwhile went away so we no longer needed to think about dropping the gear. But now we started getting a NAV ADR 2 FAULT ECAM. The ECAM would stay on a few seconds but then go away before we could accomplish any steps. This kept happening repeatedly. At one point it did stay on long enough that we were able to do the first to do step; AIR DATA SWTG(SWITCHING) - F/O 3. This seemed to help stabilize her screens; however the ECAM kept coming up but then would go away on its own before further steps could be accomplished. Eventually it stopped popping up. We did an uneventful SE ILS to just above minimums on Runway XXL in ZZZ. The fire trucks gave us the all clear and we taxied to the gate. To get three completely unrelated problems within a few minutes of each other while airborne is something that I have never personally experienced until now.