B767 air carrier pilot reported gear disagree message after takeoff. After troubleshooting; flight crew decided to return to departure airport and landed uneventfully.

Narrative

After departing ZZZ; upon gear retraction; we got a GEAR DISAGREE EICAS message with GEAR DOORS displayed beneath it. I pulled up the non-normals (757)(767) GEAR DISAGREE procedure on my EFB and the Captain requested a level off at 5;000 from ATC. We ran through the procedure up to step 6 and then the Captain transferred the controls to the First Officer and contacted Dispatch. After discussing the situation with Dispatch and Maintenance Control; we decided a return to ZZZ with an overweight landing was the best course of action and [priority handling was requested] at that time. As we began diverting back to ZZZ; the Captain took control of the aircraft back and I continued with the (757)(767) GEAR DISAGREE procedure but when we went to lower the landing gear; we received no down and locked indication for the right main gear. Ultimately; we were led to an alternate gear extension per the procedure but that still did not give us a down and locked indication on the right main gear; but the GEAR DISAGREE EICAS message blanked and was replaced with a R SIDE BRACE EICAS message. We broke off the approach at that time and requested vectors to give ourselves more time to continue trouble shooting the issue. At this point; the Captain once again transferred control to the First Officer and contacted Dispatch while I began searching for R SIDE BRACE in the FM (flight manual) but I was unsuccessful in finding the correct procedure because it is titled (767) SIDE BRACE - L (R). During this second discussion with Dispatch and Maintenance Control; they were able to direct us to the proper procedure for R SIDE BRACE which we accomplished but still did not resolve our issue. We also reviewed the Partial or Gear Up Landing Procedure. At this point; the Chief Pilot and Boeing Engineering where patched in and we were told to try several maneuvers including speeding up and slowing down as well as steep turns to attempt to lock the gear in place but nothing fixed the issue. We were advised to conduct a Tower fly-by and after completion; were told that ground crews could see all the landing gear extended but there was no way to confirm that it was locked. After the fly-by; we contacted Dispatch and Maintenance Control for a final time to report that the gear appeared to be down and the decision was made to burn off as much fuel as practicable and then return to ZZZ for landing. About 30 minutes before landing we told the flight attendants to prepare for a [priority] landing and possible evacuation. Once we were informed that that the flight attendants were ready we proceeded to the airport and safely landed without further incident on XXL. After coming to a stop; evaluation by emergency crews and company maintenance determined it was not safe to move the aircraft with passengers on board and we were all deplaned via mobile lounges.