I need to open up the mouthpiece receiver on my euph. Bassbone, large shank.

What size and taper do I need?

Probably a Morse #1. I think I need the same one for my Chinese trombone (Mirage, "large bore").

There is no commercially available reamer that's the correct size. It has to be custom ordered and as I recall the cost for one is about $250. Multiples can be made for less each, and I've considered that but never done it.

I think it's a Jarno #5. Same taper as Morse but in the size range useful for a receiver.

If it's the kind of receiver that's attached to the leadpipe as a separate piece, you could have it removed, machined on a lathe, and then re-soldered. That would be a lot simpler than tracking down a custom reamer. If it's the kind of receiver that's integral to the leadpipe, where the top of the leadpipe is expanded, it would be a lot more complicated, though.

I played the band's euph a couple of summers, and it had that intermediate size receiver. I had the local tech turn down a mouthpiece to fit. He charged so little I don't remember it.

I would think you could swap receivers for less than $250. Dumb idea I guess, but with a spare mouthpiece, lots of patience, and some grinding compound, could you do "ream" it by hand? If mouthpiece and receiver are both brass they would both wear, of course.

Alternatively, 3D print several reamers at the local library, get a tube of grinding compound at Advance Auto, and have at it. The reamers will wear out before the brass but you'll get some removal on both, that's why you need to print several.

Like drilling a mouthpiece, you'll know when you've gone too far, and have to throw away the euph and buy a new one. It's an interative process.