If "sandwiching one between two others KSP style" means horizontally, so that a FH has two more FH's on either side making nine parallel first stages, then that's an interesting question and as far as I know hasn't been asked. The closest thing would be questions about a "Falcon Quad"; a central body with four more arranged in a quad or cross-shape. For that see answers to Ballpark comparison of a hypothetical Falcon 'Quad' Heavy with cross feeds.
However, if "sandwiching one between two others KSP style" means vertically, then this won't work. A fully-fueled, un-ignited, dead-weight Falcon Heavy would be a Falcon Too-Heavy as a payload for another Falcon Heavy if sitting on the launch pad. However, yes, launched in space, a FH could certainly act as "first stage" for another FH, but presumably that's not what you mean. I think your sandwiching refers to getting a FH into space by launching it atop another FH, and that just won't work.
Another problem as @Jack points out is that the nozzles on pretty much any first stage of any kind are much smaller in maximum diameter than the would ideally be for space operation. Nozzles should expand the exhaust so that the pressure drops to something roughly similar to ambient pressure. You can't pack nine vacuum-sized nozzles in a F9 configuration. They would have to be much farther apart.
See a comparison of atmospheric nozzles and one vacuum nozzle in @RusselBorogove's excellent answer to What are the differences between a standard Merlin engine and the Merlin Vacuum engine?, as well as the question Why is the Merlin 1D Vacuum nozzle bigger than the Merlin 1D nozzle? and answer(s) there.
You might be able to get away with using atmospheric nozzles in vacuum I believe. This is not necessarily as dangerous as using a vacuum nozzle in atmosphere, but the efficiency would be compromised.
Summary: Yes, if you magically got a FH in space and fully fueled, that would be useful. However, you can not do that by putting it on top of another FH.