Are hydroxides soluble in each other?
Probably not so much calcium hydroxide, but alkali metal hydroxides mixing with each other in the liquid phase.  The pairs $\ce{LiOH-NaOH}$ and $\ce{KOH-NaOH}$ are not only fully miscible, they have been studied as fuel cell electrolytes.  The picture below, from the referenced article, shows results for the a range of electrolyte compositions that imply the extensive miscibility.  The fuel cell itself is based on carbon oxidation to carbon dioxide.