You would not want to make it softer. Despite the antimony in it, it is pretty soft already. You may want to heat treat it (in oven) to make it harder. Nevertheless, the common practice is to add a little tin (elemental tin, sheet metal is not "tin"), to make the melt flow better in the casting process....or do you need to mix it with another alloy to make it softer?
Elmer Keith and Skeeter Shelton Two of the pioneers of the modern cast bullets. Pushed a bullet of about wheel weight hardness pretty fast. I think slugging the barrel and the right lube have as much to do with good Bullets .As actual hardness. Having said that. Most loads for Rifle in my Lyman cast book recommend Lyno-type. I cast my first bullet in 1975. And one thing I have learned over the years. The variables in casting can mess a good Bullet or gun up fast. Mix of lead, Dia, of Bullet ,speed of Bullet as well as lube used.
I just bought a 55 gallon drum of wheelweights at the junkyard
Score! i just picked up a bucket full of ww's from sum tire stores... they just throw them out and said if i can convince the guys i can just put my own buckets there and pick em up weekly!!!!!
Part of what happens during cooling/solidification of WW metal is the antimony crystalizes out before the lead solidifies. The (hard) antimony is then held in the lead as a two part matrix, much like rocks in concrete, leaving the exposed soft lead to smear onto a bore more than it should. That does't matter for wheel weights but it does for bullets. A little bit of tin changes the mixture into a real alloy and that makes MUCH better bullets
Any of the older Lyman Cast Bullet handbooks are good, as is the NRA published "Cast bullets" by Harrison. It's out of print of course but Amazon's used book sellers usually have it available for reasonable prices. There is little new about bullet casting that the old guys didn't know.