Welllllll....
What you suggest is exactly what was done in black powder days. Lighter bullets went faster. .45/120 had a 300 grainer at 1600, I think.
HOWEVER, if you refer to smokeless powder then you might find the lighter bullet not providing the resistance to burn that powder correctly.
.45/70 is a black powder case design and you will find case life is less than more modern/sturdy cases. .308, etc. Please be EXTRA careful.
I think Herc, now Alliant, had a trapdoor pressure [LOW] load with Reloader 7 powder and a 300 grain bullet at 2200 fps. If you are talking dangerous game, that is another consideration. Few are wounded by deer attack. You will want a 300 grain bullet that will hold together. But they are available. Equally important, you want to be sure that the shooter can place the bullet. A miss with any bullet is still a miss. HAPPY HOLIDAYS. Luck.