If not using variant encumbrance, youYou can carry up to 15× your Strength score, or 300 pounds in your case. You can push, lift, or drag twice that, or 600 pounds. However, body weight is not usually included encumbrance: that usually only counts the weight of objects you carry, not your own weight. So at least by the rules, the answer to this question doesn’t really matter.
But we can still answer the other side of the equation, very roughly:
Platinum has a density of 21.45 grams per cubic centimeter.
This study in the Journal of Diabetes Science and Technology, finds that the mean volume for their sample of human male torsos is 65.66 L, or 65,660 cm³. Note that this study defines “torso” as being from the total body volume (per a 3D scanner), minus the volume of the head, arms, and legs.
Also note that this study was specifically a comparison of Caucasian and Hispanic adults, and all subjects came from in or around New York City. Other ethnicities or geographical regions were not included in their average. Global averages may well vary significantly from this finding (I saw a less-rigorous estimate of just 47 L, for example).
That gives us a weight of approximately 3,250 pounds, vastly in excess of 300 pounds.
(The 47 L estimate, by the way, results in 2,222 pounds—also much greater than 300 pounds.)
This implies that—just as your torso is clearly magical because it continues to function as a torso—something magical is going on allowing you to move around. Maybe it’s magically-light platinum, or your body muscles are magically strengthened in some very specific way that allows you to carry your own weight but not otherwise count as having a higher Strength score, or there’s some magical anti-gravity effect, or whatever.
The Strength score required to move 3,250 pounds around comfortably is 217. This would limit your gear pretty significantly, though; you’d probably want something closer to Str 225 if you were actually carrying all that weight around by the rules. (For the 47 L estimate, it’d be Str 150, but probably more like 160 just so you can also carry other stuff.)
- Note that 3.5e used different numbers for these things in general; a 200-pound heavy load would be Strength 15 rather than Strength 20 in that edition.