If the regulator overheats it should shutdown - so I'd say you can run at 7.4V, the regulator will be hot, not ideal but unless it shuts itself down this can be tolerated. 11.1V sounds right out (it will be causing about 2 1/2 times more heating in the regulator).
If you'd like those 11.1V for some other reason then an external 5V regulator with a proper heatsink, or a little switchmode DC->DC converter are the options. The latter is more efficient / cooler, but will put a little noise on the 5V rail in my experience (only as issue for analog sensing).