I'm not sure of the reason for the question. No question it can be done. Lasse Karlsson has a video of him casting a 12 wt Rio Outbound on a 3 wt, 6'6" Echo Rod (particularly noted for their strength).
Note how low the end of the line is as it comes by him on the forward cast.
As I recall, he was able to cast further with the 12wt than with a 3wt that day on that rod. But how often do you need to cast a 3 wt line 90 or 100 feet?
Like Swirl, I have broken only 2 rods while casting. One was an overlined rod a friend wanted me to cast to see how far it would cast. It snapped on the first presentation cast. I have refused to do that from that day on. The other was one of my own rods that was very well used, and I was really, really pushing it, though it was not overlined. It undoubetedly had gotten a ding or 10 over its lifetime.
I've played more with underlining than overlining, and prefer long heads to short - and the reason is so I can fine-tune the line weight by varying line weight outside the tip, among other reasons.
Although this is heresy of the highest order, I don't subscribe to the "load the rod more" theory for short casts. I subscribe to the "match the line weight/taper to the conditions (including fly/popper size/weight/wind resistance/fish species), and the rod to the line weight" theory.
Nor do I suscribe to the theory that overlining slows the "action" of a fast rod. What it does is cause it to load lower down. I think people confuse "stiffness" with "action". The "stiffer" the rod, the "slower" it is - regardless of its rebound speed. I think the terms "slow" and "fast" are poor words to describe the action and "tip-flex' etc. are much more explicit and less confusing.
I have a very stiff slow-action 12wt.RPLX rod which I "overline" with the old tarpon taper Rio 12 wt. That particular line is too heavy for my xi3 for me. I fish either a 10wt Cortland Liquid floating or a 11 wt liguid floating on that rod depending on the wind and fly.
One perfect casting day I was distance practicing, casting line weights from 4 wt to 8 wt on a Sage TCR 8wt with an ERN of over a 10 wt. All but the 4 and 8 wts were SA MED lines. The 4 and 8 wts were old unknown brand WFs. It cast well, but the rod vibration got my elbow bones to chattering and was a painful experience that I would not do again. My longest casts came with a 6 wt MED on that rod. If it were blowing slightly I'd use a seven MED, more wind and I use a shorter head (than an MED) in a seven.
But even with a short billfish line, I get the most comfortable results with an overhang of almost exactly half the head length in runing line outside the tip for longish casts. For sight fishing or casting to spooky fish, I use the lightest line that's comfortable to cast.
So if an 11 wt on a 6 wt rod is the most comfortable for you, then use it.