How Japan could stretch the destroyer label beyond Izumo

After calling the Izumo aviation ships destroyers, what could Japan designate as a destroyer next?

Most plausibly a very large missile-heavy air-defense combatant; the label would be political, and nuclear propulsion is only a speculative extension.

The proposed Japanese ship would again be called a destroyer. An aviation ship substantially beyond Izumo would stretch that description, so the answer turns to a very large missile combatant instead. Sejong the Great provides a comparison for how far a missile destroyer can grow. The speculative extension is nuclear propulsion and a very large missile battery, presented as additional air defense for Japan. The answer distinguishes this imagined ship from the large Japanese combatant then being discussed, which was not nuclear-powered.