In reply to Pj84:
Hi Adam,
Last summer, three friends and I did exactly this. We flew into Khan Tengri base camp on the North Inylchek glacier, and from there trekked about 10km down the glacier (to the West), where we set up a camp. There are a number of unclimbed peaks there, we climbed Peak 5023m on the southern side of the glacier. If you're interested here's a video:
There were a number of unclimbed peaks of similar height on the north side which looked potentially climbable, but we ran out of time to do these, so they could be good objectives for you. Razor Peak at the very bottom end of the glacier is also unclimbed, but would take a few days to walk to from the base camp.
Hope that's of some use,
Cameron