Maybe I'm misunderstanding terminology here.
A step chuck uses a standard collet closer but provides work holding larger than maximum size normally allowed by the collet system, with the limitation that the work being held can go through the back of the collet because of the step.
At least that’s what I see with the step chucks for my clockmaker's lathe, and what I see Hardinge selling for 5C, etc., applications.
This doesn’t use the collet system provided by the lathe, but screws into the spindle just like a regular lathe chuck. So, I am calling it a collet chuck, but the collets are through collets. Of course, the spindle is too small for most of the sizes of collets I have for this thing, but that's not the collet chuck's fault.
I'd be really curious to know the history of this lathe and why some past owner felt this chuck was necessary. All I know is that the lathe was sold in 1945 to the "Elec Sup" at Bethlehem Steel's huge (for the day) plant at Sparrow's Point, MD. And sometime later it was owned by an aircraft mechanic who used it either making or repairing propeller parts. He was the immediate predecessor to the person I bought it from (who is also an aircraft mechanic, but who bought the lathe as a hobby). I suspect this chuck was needed by the guy dealing with airplane propeller parts. I have no idea what accuracy he needed, but I'll bet a +/- 0.001 would be pretty good for most of it, except bearing journals.
I also suspect that the idea behind the sleeves for the main tapered collet is that the sleeves are far easier to make. It could be that making the taper in the shop was enough more difficult that getting one good tapered collet and then using sleeves was the shortest path to the required accuracy. What I have not done (yet) is to measure the wall thickness of those sleeves using a tubing mic to see how concentric they are. I'll wait on that until the TIR is too large for a project, if that happens.
Rick "a lot quicker to get to 0.001 than using the four-jaw for smaller parts" Denney