In the November, 2014 issue of the Proceedings, Lieutenant Colonel J. Noel Williams (USMC Ret.) lays out a case for combining the SSC/Frigate role with an amphibious ship. He calls it a Frigate Helicopter Dock.
The LCS and the LSD should be replaced by a new class of surface combatant, which could be called the frigate helicopter dock (FHD). 4 Such a vessel would provide robust interfaces to all physical domains: to the surface and subsurface through a well deck, and to the air through a flight deck. It would also add substantially to the offensive striking power of the Fleet with a 48-cell vertical launch system (VLS) and a 5-inch gun. Chief of Naval Operations Admiral Jonathan Greenert is correct to emphasize the importance of payloads, and the FHD would provide nearly infinite payload possibilities.
His concept is for a ~10,000 ton ship. However since steel is cheap and air is free, I endeavored to draw up a larger variant.
Why do such a nutty thing? Well, if you can build one vessel that can perform both roles, then you can buy more of them and achieve greater economies of scale. Also, a large ship is far more flexible across a range of missions than small ships like the LCS.
Price is obviously a big question. If priced like an LPD (per thousand tons of light displacement), it could go for as "little" as $1.1 billion. If priced like a DDG-51, it would be an unaffordable $2.7 billion.
Anyway, here's the drawing. I started with the ThyssenKrupp Marine Systems MHD-150 design, because it roughly fit the size and configuration I was looking for. I made obvious modifications.
(Edit: Image altered to reflect comments)