Air carrier First officer reported #2 Engine vibration during climb out. The flight crew completed an air turn back and precautionary landing at destination airport.

Narrative

The flight operated from ZZZ-ZZZZ1 at 392;000 Kilograms total weight. 144;000 Kilograms fuel onboard. The weather was -1C and snowing. The aircraft departed late for maintenance reasons; and the load was lobster that required Maintenance to fix the temp control in the forward lower cargo area. The issue was added as a deferred item; and we started the de-icing process; which took an abnormal two hours to complete. After the first application of de-icing; the aircraft accumulated so much snow that they had to deice again. During this time; Aircraft Y returned to deice again as well. After our second round of de-icing; our hold-over table showed us having approximately 20 minutes of holdover time left. Were taxied to and held short of Runway XX/full length. Holding short of Runway XX; the aircraft in front of us returned to the gate to get de-iced again as well. We still had time left on our holdover but decided to conduct a visual contamination check by the 4th-seat FO (First Officer); who said the aircraft was contamination-free.Cleared for takeoff; we executed a 60% run-up for 30 seconds. With normal engine indications; we took off max thrust / NADP 1. We were handed off to Departure and cleared direct fix ZZZZZ with instructions to climb to and maintain FL200. At 1;500 ft. thrust was reduced per the profile and immediately the vibration monitor came up on the lower EICAS; and Engine # 2 and showed a level of 5. One second later there were numerous loud bangs and flashes of light outside the aircraft. The compressor on Engine #2 stalled; however from what I could see in the observer's seat; there were no abnormal engine indications. I informed the crew to use me as needed and immediately reached for the QRH to be ready and turned to the appropriate page for a compressor stall. The Captain seeing strong vibrations retarded Engine #2 thrust to idle to get the vibrations under control fearing immediate harm to the aircraft. The First Officer continued to fly the aircraft and called for immediate action items. We did not have another compressor stall and there were no more indications of anything immediately dangerous to the aircraft. The engine was still operating at idle. The aircraft flew well and we requested 15;000 ft. level-off while running the Engine Limit or Surge or Stall checklist. As we followed the checklist; it gets to a point of if all indications are normal slowly advance the thrust lever. All engine indications seemed normal except the N2 vibration quickly increased back up to 5; so the Captain pulled #2 thrust back to idle; but this time the vibration stayed at 5.After finishing the checklist and the QRH; we requested to dump fuel so we could return to ZZZ not being able to continue on three engines at normal power and one at idle. We held for over an hour dumping fuel and we discussed the part of the checklist where it gives give you guidelines to decide if the engine should be shut down or continue to run at reduced thrust. Since EGT was normal and we were very heavy; we decided to leave the engine running at idle in case we needed it during landing or a go-around or if another engine or two started acting up; as the cause was still unknown. We finished our fuel dump and conducted an auto-land for a safe return to the ramp. By the time we got back to the blocks; Engine #2 had been running at idle with engine anti-ice on for about 1.5 hours; and Maintenance still found ice inside when they opened the cowling; noting that it was highly unusual. The Captain and my two fellow First Officers were calm; composed; and professional during the whole event. I give them all my highest praise for flying the aircraft as FO; the Captain for commanding the aircraft to what I would consider the highest level of professionalism and knowledge; and the fourth seat FO for backing me up with confidence and composure so that we could give everything needed to the PF (Pilot Flying) and PM (Pilot Monitoring) to get the aircraftsafely back on the ground.