Saturation of multiple solutes
Different solutes in the same solution indeed can affect each others' solubility. One example where this effect can be used to advantage is the "salting out" of a protein from water solution. Adding a salt (ammonium sulfate is especially good for this purpose) reduces the solubility of the protein in water, causing it to precipitate or crystallize out. Salting out can also be used to more fully separate an organic solvent from water. I imagine that in your example with the sugar alcohols, adding one component to water will reduce the solubility of the second component by a similar degree. But there may be cases where one solute increases the solubility of another.