How can you increase the solubility of most solids in water?

The only effective way to do that is to heat the water.

Others may come along and tell you to crush the solid into tiny pieces, or stir the water or shake the jar while the solid is dissolving. Those actions can make the solid dissolve faster, but they don't change the amount of solid that eventually dissolves if you wait long enough. The only way I can think of to do that is to make the water warmer.