The .577/.500 3 1/8" Magnum is yet another base and rim dimension; slightly smaller than .577NE and larger than .500 No.2, hence still the same problem with .500 No.2 in a Snider shellholder.

The nominal dimensions of the .577 Snider base and rim diameter are the same as .577NE with the Snider having a .065" thick rim while the .577NE has a .055" thick rim. The .577/.500 Magnum would be less sloppy fit by some thousands.

A "proper" shellholder for the .500 No.2 is a one of a kind beast.........pity that RCBS used to be known for "proper" and boasted "precisioneered" as opposed to "yep, close enough for the average rube".
- Mike