Peter, You can get MT sleeves that step up, not only ones that step down.. Porta And Dormer are two manufacturers and there will no doubt be others. Any good engineering tool supplier should have.[ maybe not as a stock item] but will order.

Am with you now, Yes, you do get step up sleeves from MT3 to MT4 but you would need one that is open [through the MT3 until the MT4 ] so that you can hold both the chuck AND the sleeve with a drawbar. Thats going to result in the end mill being a long way out from the spindle nose.

Cutting down the taper might be feasible id the lathe is rigid enough. Ideally the taper would be finish ground. Depending in the existing draw bar thread size, it could be a challenge getting in new draw bar threads compatible with the 3MT. An extension adapter that jumped from MT3 to MT4 would not be feasible for at least two reasons: that type of extension holder has no provision to pass a draw bar through it; he length of that extension, in addition to using up spindle to table clearance, would result in a too stickout (from the spindle face) that would severely limit the ability to take a cut.

In short, using an extension adapter is not going to work due to problems retaining the tool and the lack of rigidity would render the arrangement nearly useless.

Go ahead with your plans to turn down the shank of your holder. If your lathe is not up to the task, find someone with a larger lathe to help out. If possible find someone with an OD grinder or toolpost grinder to finish the taper. You can figure out some way to adapt the drawbar threads.

It is possible that you can turn down the taper. Some years ago I had a load of 22 mm drills & a reamer from a skip , all with tapered shanks. I turned half a dozen down to half inch parallel to use in a jacobs chuck. Still have one .

Could you cut one to fit say a 5/8 collet or is that too much of a bodge for a model engineer?

Annealing HSS is next to impossible with home shop equipment. As this taper is going up the spout of a milling machine it needs to be spot on. I'd invest in a ER32 chuck on MT3 taper and sell the MT4 one on e-bay. This despite my Yorkshire ancestry

Well, i dunno, i've managed to screw cut HSS endmills to fit an auto-lock chuck in the past and i heated them up and let them settle. I've got no idea what sort of nightmare you'd be in for if you tried to mill it. I've also cut HSS things to size using this method too. You're probably right though, if it means large chunks of it.

I'd agree this probably ain't worth the fuss of making this socket unless you're a die hard home maker. Whatever floats your boat i guess.