We have found that jacketed bullets can be sized (drawn) down about .003" safely, in Lee dies.

Some years back, a friend bought 3 Lee die sets to size .338" bullets down to .323" for his 8x68S, as well as .323" bullets down to .314" for his P-14 Enfield in .303.
9.3x57 (Rod) of this site was also into sizing down .375" bullets to .366" at that time, as I was too.
A "good" lubricant is needed. I found Imperial sizing wax was good, as-was STOS, a Ponsness Warren lubricant for their shotshell loading presses.
Most ctg. chambers and cases will allow bullets from .001" to .002 oversize, without increasing breech pressures, especially with cast bullets.
If the larger bullet will fit/slide into a just-fired case, they can be loaded without being sized smaller.
For example, my old 9.3x57 would accept jacketed bullets up to .367"(sized down .375's) which all shot into sub 1" at 100 meters.