Say that a minor navy is looking to rebuild their early battlecruiser they have for whatever reason (Invincible, Indefatigable, Von der Tann, Moltke, Seydlitz) in the early 1930s and that money is no real issue, they have the cash to get the ship to the greatest level of modernization possible but not enough money or connections to afford to build or buy a more modern capital ship. And that this navy decides they still want the prestige of having a capital unit floating around and so dont just buy some cruisers with the money instead, maybe some cruisers are bought anyway.
Aside from the obvious things, converting to oil firing, boosting their speed, upping their armor and torpedo defenses, what other things could be done with such a hull. You could remove the casemated secondaries, but with a ship using en echelon turrets you wont have the room to add turreted secondaries, increasing the elevation of the main guns would be welcome, as would fitting out of new rangefinding equippment.
Really the biggest issue with these early battlecruisers, and some battleships, is their odd turret arrangement as it limits what could be fitted on the upper deck. But could you add say a meaningful AA battery to the ships by building up the superstructure and funnels with plenty of places to squeeze in guns and rangefinders in the 20-40mm range?