You should find the Load & Inflation Tables for that particular tire, but here are some general guidelines, from my notes:
A 10 ply MPT in 275/80R20 can carry #3300 per tire @ 35 psi on grassland, at speeds up to 30 MPH. It can carry #3300 per tire @ 22 psi in mud/sand, at speeds up to 12 MPH. A 12 ply 335/80R20 carries #3600 at 30 psi and 30 mph on grassland, #3600 at 16 psi at 12 MPH in mud or sand. An MPT80 clears mud well, but an MPT81 is probably better everywhere else. (37.4” diameter) These tires are heavy in 14 – 16 ply.
335 MPT 81 is only available in 22 ply, a 68 MPH speed rating and #6700 load rating. A 335 MPT 80 is said to be quieter on road, but not as good off road, except for mud. A 10PR military version is available, rated at #3960 and 62 MPH.
An XZL MPT in 335 will carry #4400 per axle at 18 PSI at speeds up to 45 MPH on hard surfaces. For short sand/mud stages, 10 PSI can be used at a #5500 axle weight at a maximum speed of 10 MPH. For dirt road stages, at speeds of 35 mph or less, with a #4400 axle weight, 16 PSI should be used.
EDIT: The numbers below provide what the tire is rated to hold at a given pressure. This is likely under ideal conditions and should be taken with a pinch of salt.
Toyo Mud Terrain in 37x12.50R20E: #1930 (25 psi), #2225 (30 psi), #2470 (35 psi), #2705 (40 psi), #2925 (45 psi), #3085 (50 psi), #3335 (55 psi), #3525 (60 psi), #3750 (65 psi)
Toyo Mud Terrain in 37X12.50R18E: #2095 (25 psi), #2395 (30 psi), #2680 (35 psi), #2915 (40 psi), #3150 (45 psi), #3415 (50 psi), #3590 (55 psi), #3795 (60 psi), #3970 (65 psi)
Toyo Mud Terrain in 40X13.50R20LT: #2470 (25), #2815 (30), #3085 (35), #3425 (40), #3705 (45), #3970 (50 psi in D load range), #3970 at 55 psi – 65 psi for E load range.