Interesting...
From the sketch (on standard K&E graph paper, yet!), it appears the same engine was used on all three stages, just less nozzles on the upper stages. I remember seeing the Bonestells of these vehicles and it always struck me, "why so many little engines when a few big ones could do the job"? I guess the answers are 1) redundancy and 2) you minimize risk with a smaller, single, easier to engineer design, and you simply use many of the best ones available once you get all the bugs out.