Using a current design essentially means a modified Arleigh Burke hull. I don’t know how feasible it would be to make these ships larger to hold more stuff. The big question is whether a longer and perhaps wider Arleigh Burke class DDG can handle much more in the way of advanced weapons and sensors as effectively as a new design can while being more capable of surviving in a combat zone.
Put this in your Naval Architect pipe and smoke it: How about, since we are already building them, using an America Class LPH hull as the basis for one of these bad boys?
844’ x 106’ ought to provide enough room, you think?
https://en.wikipedia.org/wiki/America-class_amphibious_assault_ship