Unique, Universal, and AA #5 probably come as close as you’re going to get as usable for all three. It’s ideal for 38 Special, a bit slow for 380 and quite a bit slow for 357 Mag if you are indeed wanting to wring out every bit of potential from it. If all you want is a +p 38 Special out of your 357, Unique and Universal will do nicely. Otherwise Blue Dot, H-110, 296, and AA-#9 and Enforcer will far better choices. 380 is better served with the likes of Titegroup, AA-#2, 700X, and similar burn speed powders.
Reasons why, 380 is small capacity, medium velocity, light weight bullets, 38 Special is a mid range round, not high pressure or high velocity, nor generally heavy bullets. 357 is a high pressure cartridge that performs at significantly higher velocity and has greater powder capacity with both medium and heavy for caliber bullets.
A little study of several load data sources will show you this. I load all three plus another dozen handgun chamberings and have many, many different powders for them. It became obvious in a hurry that only one powder will not do justice to 3 completely different types of chamberings even though they are all three basically 9mm/ 38 caliber rounds. To make it more interesting, toss in a 357 SIG, 9 Makarov and 9 Luger into the mix,