I was looking in the lyman blackpowder handbook and they have charts for 370gr Maxi balls with 120gr of goex and 20k pressure that seems way too high for a non inline muzzleloader.
What is the maximum pressure for a Great Plains rifle with a 1-32 twist, brand new one?

I don't know what the maximum pressure might be, but I do know I don't want to shoot a GPR loaded with a 370 gr. Maxi and 120 gr. of BP!!! I have become pretty inured to recoil thru the years, but having owned a GPR for many years I would call that a shoulder-destroyer in that rifle. It would hurt me so bad I wouldn't be able to scream! That crescent butt -- OWWWWWW!!!!!!

PS I feel that's too high-pressure a load, as well, and would stick to something considerably more sedate for safety's sake. Certainly no more than 100 gr, and that's still a heavy load in all respects.

Lyman uses good metal in barrel and it is not going to think about bursting at 20K PSI but the problem you get into with a side lock/traditional percussion is that as pressure climbs you get more blow back through nipple. When this blow back gets strong enough to return hammer to half cock from pressure jet through nipple, you are getting a bit to warm. (not be cause of bursting but blow back danger) I might add that the 370 maxi is deadly at close range but runs out of gas with range and drops a lot and once you get to 100 grains or so with it, you are not going to kill it any deader or get any more range out of it to speak of with more powder in that gun/bullet combo so why waste the effort.

I can't imagine Lyman publishing loads that would be unsafe for their rifles. My 54 caliber GPR was one of the old round ball twist guns and it's been gone for a lot of years now, but it sure was a dandy deer gun with one of those patched round balls out of that slow twist barrel at the time.

If your going for elk than perhaps max loads are needed but for deer I agree with pisgah, that long drop stock can really beat you.

It is very hard to over pressure a 54 with a round ball. The rate of expansion of volume in bore is such with a RB and a slow twist that pressure are below 10k. Lyman's latest Black Powder Handbook list 8300 PSI for a 54 RB with a 32 inch barrel with a 1/60 twist with both 2FF and 3FF. 120 grain of Pyrodex RS yield only 7100 PSI. so you can safely go well beyond 120 if you desire with a RB. (slow 1/60 to 1/72 twist have less pressure because bullet is not taking as much energy to be spun up as quickly. A 1/48 twist peaks at about 11000 with same loads. Even heavy conical 120 loads stay at 15000 or less in a 54 with few loads exceeding that with a 1/48 twist. A 530 grain maxi shows 14400 PSI with 120 grains of 2FF yet with a 1/32 it can hit 19000 PSI. It appears that sabot load have more drag in bore and a 330 grain one can peak at over 17000 with FF and 19000 with RS. 50's are different matter because with heavy conicals you can exceed 20000 with 100 grains of powder with several bullet styles. On the average 50 cal RB load run 60 to 90% higher pressure with same powder charge than 54's do. iN A 58, even 140 grains of FF yields only about 9000 PSI with a RB in a 1/48 twist.