It looks like a custom size die for a Lyman/RCBS lubri-sizer except for not having a groove for the retaining set screw. without any other information or dimensions that is all I can think of.
That a sizing die for the mx3 series bullets. Specifically the mx3-32s.
Egan made several molds with the long tapered multi lube grooved bullets. They were designed to fit the leade angle in the custom and common cartridges. 1*, 1.5*. 2* etc.
This egan mx3-30 us does extremely well in my 308w. I do have the correct t-30 sizing die for this mold.
I've had an Eagan .30 caliber taper die for 25-30 years. These dies appear to be in demand. You might check cast bullet sites if you have no use for the die and choose to sell.
I don't think you can (if you want good accuracy) but I'm not sure I understand your question. As an example, the Lyman #314299 design is .30 caliber and the unsized bullet base will measure about .312" to .314". I generally size these in a .311" die.