Older Hornady micrometer seating die caliber id?

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So I picked up some reloading gear at a garage sale recently, cool old square metal powder cans, manuals from the 70's etc.
Among these things is this remarkably unmarked seating die. As best I can tell it's a Hornady micrometer seating die but no markings at all, on anything (except numbers on the dial of course). Looks complete but figuring out the caliber is challenging.

My micrometer tells me the seating stem outside diameter = 6.12mm or .241 in
The inside diameter of the sleeve where the neck goes in = roughly 7.05mm or .277 in
A possible clue is the shell holder that was in the press with the die (assuming they were correct) is a RCBS #4 so maybe a magnum cartridge? But smallish neck?

Before trial end erroring thru my collection of various brass I thought I would consult the wisdom of the castboolits board for any tips or hints as to what I've got.
Picture to show details & both ends of the sleeve.
Thank you all in advance for your help.

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Update:
I grabbed a 243 Win cartridge I had handy and it fits the sleeve pretty well:
6.16mm bullet diameter
7.10mm ish neck outside diameter

This rules out the shell holder though, rim is a bit too small for the #4 holder.

Not being familiar with these dies I'm not sure how much tolerance to expect.
Is the sleeve meant to contact the shoulder?
Are they made to use in a range of cartridges?
Thanks again in advance for any insights.

[racepres]

I have numerous sliding "guides" and seating stems..for various cartridge diameters..308 for instance is the one sliding Sleeve, that has a couple seating stems for various boolit profiles. yet the same setup is used for whatever 30 Cl, I am loading. Never gave problems when die is adjusted properly.. Tho some sleeves do incorporate a Crimp shoulder..it is Much like using 44 mag in a 44 Special die!!! If the shoulder is contacted...you have mis-adjusted...

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Thank you race for your reply, certainly helps me understand this guy better. Mag vs Special makes sense to me. I do like the idea of a multi-caliber die with interchangeable sleeves.
I'll just have to try it out and see what I get. Pretty cool to accidently be introduced to something new and learn a bit.

[racepres]

Thank you race for your reply, certainly helps me understand this guy better. Mag vs Special makes sense to me. I do like the idea of a multi-caliber die with interchangeable sleeves.
I'll just have to try it out and see what I get. Pretty cool to accidently be introduced to something new and learn a bit.

I have a "bench mounted holder" with various "sleeves", some even for different length necks! A couple "bodies" and yer all set for Multiple Cartridges. By all means...try it some, me thinks you will like it..tho I sometimes use a Factory Crimp on certain loadings...Nuther operation...but....
Good Luck

Edit; BTW too much neck expansion inhibits the sleeve from coming over neck like it is intended to (as a Guide), but, M-die does Not seem to be any problem.