The modules are too large for the ship's existing vertical launch cells, so they would likely take the place of its all but abandoned deck guns.
The U.S. Navy is now officially looking into what it would take to arm its Zumwalt class stealth destroyers, also referred to as DDG-1000s, with hypersonic missiles. The service has also now disclosed that it is looking to field these missiles loaded into an Advanced Payload Module, or APM, that has "a three-pack configuration."
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Update: Navy searches for companies able to integrate hypersonic weapons aboard Navy Zumwalt-class destroyers (Military and Aerospace Electronics)
WNU Editor: The US Navy is also looking at putting lasers on the Zumwalt destroyer .... The Navy Wants to Put Lasers on Zumwalt Destroyers (Popular Mechanics).