Well, you maybe have a half a hole between the .243 and the '06. Personally, I've never felt the need to fill that same hole in my own inventory. Aw, there've been the occasional .308s or .257 Roberts sort of stuff; but they were more "instead of", rather than "as well as".
Particularly if you handload, you might consider the 7X57 or the 7mm-08. Bullet weight and energy lie right in between the .243 and the '06. Generally, you don't have a lot of use for stuff like the .25-'06 or a .264/7mm Magnum.
Dunno what kind of .22 you have, but an upgrade there is never a bad thing. .22 tack-drivers are Good Things.
FWIW, Art