I suspect that you have searched the net for info .... but here goes anyway. Unless you have a custom barrel made, then the TC, CVA, NEF, H&R , etc. standard chamberings that are 35 cal. or larger are limited to a handful .... if I recall correctly, which at my age is a question, the 44 Mag., 45/70 Gov., 444 Marlin and 375 H&H are about it.

Of these I have first hand experience in center fired rifles chambered for the 44 Mag., 45/70 and 444.

I have a Marlin "Guide" in 444 Marlin and love it. But a wiser choice of these 4 cartridges in my opinion is the 45/70 Gov. The 44 Mag.'s effective range is just too limited in my book. The 35 H&H is way beyond the pall for deer sized game, and I can only imagine the recoil ! Factory ammo for the 45/70 is much easier to find than the 444 Marlin stuff. (If you hand load , then I'd say these two are about even.)

If you go for the 45/70 Gov. cartridge, be sure to try the Hornady "Leverlution" stuff. Shoots great out of my Guide and is a rock solid deer and hog killer from near point blank to 160-165 yards (longest shot I have taken with my Guide gun). I have killed feral hogs and deer at 20 yards or less, with full pass throughs for sure and no evidence of jacket separation. The 160 +/- yard shot was a hold over because my rifle is dead on at 75 by choice. The hit was a tad high, but the nice buck fell dead within 30 yards or so. The bullet was found under the skin on the ff side .... nearly perfectly mushroomed.