Since 4 engine commercial jet airliners started flying in the 1960s I cannot think of one accident on a 4 engined jet airliner due to multiple engine failure resulting in insufficient thrust to remain airborne. I am not counting fuel exhaustion as those were not mechanical failures of the engine.
I can think of one: El Al 1862 at AMS on 04-10-1992, though why it eventually crashed was damage tot the leading edge device. Loss of engines was not exactly independant though...