I'd probably step up in size, since you already have a .270win, which is a great medium size deer type round...
step up to a magnum.... I think on the low end I'd choose a .300wsm all the way up to a .375H&H which is argued to be the most useable cartridge in the world....can hunt the world with it...
I think I'd strongly look at the...
.300 WSM or Win.Mag.
.300 RUM
.338 Win.Mag. (very versatile from deer to brown bear...and my pick/suggestion that you get)
.375H&H