Im 99% there isn't. AM data is for sure a thing and allowed however, but it would need to be a customodulation scheme I think, I don't know of any off the top of my head. You also would run into the same carrier width restrictions, so in reality, you would have half as much signal I think.
Discussion
Well, AM is wider bandwidth than signal sideband because AM is basically a double sideband, but I do believe that what's on one is mirrored on the other, so you'd be losing signal strength and not getting any more data through, which would be unfortunate.
With single sideband, all of your power is going into a smaller bandwidth which makes it travel further distance.
Correct. What I mean is that currently, the FCC limit is 2.8khz for data modes. So on am, you would need a 1.4khz signal on each side, minus the carrier signal. So it doesn't really help. On VHF frequencies you can just use fm modes at a much higher rate. With the tradeoff of less range of course.
Oh, okay. I see what you mean now.