Are hydroxides soluble in each other? Let's say I have molten potassium hydroxide and then I add some Calcium hydroxide. I imagine, since there are hydroxide groups floating around, it would be energetically neutral for the calcium ions to bind to a "new" hydroxide group, therefore they should be floating freely with the hydroxide groups, becoming solvated. I can't find any empirical data; is my reasoning correct and I can dissolve a hydroxide in any other molten hydroxide?
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.