B767 Captain reported Stabilizer Trim and multiple autopilot problems during initial climb. The flight crew coordinated with Maintenance and ATC and performed an air turn back and precautionary landing at departure airport.

Narrative

Passing 10;000 feet near ZZZZZ and climbing the EICAS displayed Stab Trim while hand flying. Relief Pilot reviewed the QRH; and the light extinguished after about a minute. It appeared transitory and stayed off; so we continued turning on the L Autopilot. After a couple of minutes; the EICAS Stab Trim and L Autopilot displayed. The autopilot was disconnected and the EICAS message went out after about 20 seconds. After some discussion we engaged the C Autopilot and a few minutes later the EICAS Stab Trim and Autopilot displayed again. The Autopilot was disconnected and after discussing the situation with Dispatch and Maintenance; the discussion was if it happens again; a return to ZZZ was the safest course of action. the C Autopilot was engaged and a couple minutes later; the EICAS Autopilot displayed (no Stab Trim). The event record was pressed for either the 1st or 2nd time the EICAS alerted. Also noticed; the C Autopilot would not bank greater than15 degrees for any turns in LNAV or HDG SEL modes while the bank angle was set to auto position. We returned to ZZZ.