The Boeing 747 can carry a fifth engine on the side. As the airframe looks quite symmetric, I think that it would not be big work to hang a sixth engine on the side as well.
From here, we seem to be quite near to the six-engine aircraft - a few extra pipes and wires are probably all we need to get these engines turning.
Was a six-engine 747 present at some time of its development history? I think this could be, assuming:
- less powerful engines than eventually were available
- maybe it could take off with less runway
- some special uses with very heavy payload.
There are no six-engine variants mentioned, built or proposed, on Wikipedia.
The expected answer would mention some sources relevant to the design decisions through the history of this aircraft.