yep, you CAN use higher order modes.
You run the risk of your energy propagating down the guide in more than one mode, though, and that would cause havoc in some systems. In a communications system, it would look like a constant dispersive fade.
If you wanted to run a TE20 mode, you could probably do it safely if you SUPPRESSED the TE10 mode, with screws or a septum. A guide with a TE20 mode, would have the left energy at 0 degrees, and the right energy at 180 degrees....so it might make a perfect broadband balun, for instance