I have a set up which does pretty much what this chap is asking, although I am starting to move into recording three people at once instead of multi-tracking everyone individually. However, so far, that's all I've done - record drums, then bass, then guitars, then vocals. I've got a Yamaha MG 12/4 with six mics going in from the drums.
The bass drum and snare drum go from the mixer to channels one and two on a Delta 44 via the insert i/o jacks, and the cymbals and toms get mixed down to a stereo pair which is routed through the stereo out into channels three and four of the Delta 44. It works excellently, although I have now bought another Delta 44 so I don't have to put the cymbals and toms on the same stereo track, the bass drum and snare still go through insert i/o jacks to inputs one and two on the first Delta 44, the toms get routed to the group out and sent to inputs three and four on the first Delta 44, and the cymbals get routed to the stereo output to channels one and two on the second Delta 44.
Of course, all that could be summed up by saying: you can do what you want to do with a Yamaha MG 12/4 (or equivalent mixer) and an M-Audio Delta 44.