Considering your current firearms I would recommend a .30-06 or .308 Win for your seond big game rifle.My preference would the .30-06.

If you like exotic you could get a .280 AI. Very close to the same thing.

I would recommend you avoid magnums at this point. They are heavier, more costly and give little for all that bother.

After the .30-06 I would step up to a .338 Win mag and finally to a .375 H&H/375 Weatherby.