Most people accept the .30-06 as being an all around cartridge suitable for any game up to Black Bear, Elk, and Moose. Some prefer something bigger if Grizzly Bear and Brown Bear are the intended quarry. The .308 that you have is considered to be a little less powerful than the .30-06, but I get the impression that this edge is not discernible until you start looking at using 220 grain bullets in the .30-06 where its greater case capacity may be used to advantage. For practical purposes, it is likely that your .308 is entirely suitable out to 300 yards for Black Bear, Elk, and Moose and slighter creatures. If you are concerned at this limit, investing more time in marksmanship and stalking skill would likely pay greater practical dividends than buying a rifle chambered in a heavier cartridge.

Of course, I am not discouraging you from buying rifles in other cartridges in addition to your present rifles. If you are inclined and able to purchase additional rifles, by all means go to it man! But don't feel like you are handicapped in hunting the species identified above if you can't buy a special purpose rifle.