Almost any oxide cut under the cap will -increase- bottom
plate capacitance, by reducing Tox(). However in a non-
planarized technology you might be able to -increase-
the Tox() by surrounding the cap with rings of poly and
metal, making the spin-on-glass "pond up". But then you
would pick up these fringing capacitances.
A bottom plate that is electrically distinct, but co-driven,
would not reduce capacitance per se but will minimize the
charge transferred and leakage. Kinda like triax cable is
used for low leakage DC measurements. Not likely a good
plan for RF, but OK for stuff like analog sampling.