The 6mm she already owns is capable of about 100 fps greater MV than the 243, when hand loaded, and uses the same diameter bullet. Therefore, technically speaking, for her to buy a 243 would be a (very small) step backward.
To go up the power scale (rather than down slightly) it would go something like this: 257 Roberts (uses same capacity case as 6mm Rem/7X57 Mauser)
260 Rem (uses same capacity case as 243/308)
25-06 (uses same capacity case as 30-06)
7mm-08 (uses same capacity case as 243/308)
7X57 Mauser (same capacity case as 6mm Rem/257 Roberts)
Anything bigger would be too much recoil, for sure.
The 7X57, in factory 139/140 grain loads will have less recoil than the 7-08 factory loads of the same bullet weight, because the MV is about 200 fps slower that the MV of the 7-08. Still good to 200 yards, though. The 7X57 can be hand loaded to 100 fps faster than the 7-08, but then the recoil is increased. Makes it a 300 yard load, also.
Artillery lends dignity to what would otherwise be but a vulgar brawl.