Does this... exist? I mean, has it been named, or enumerated anywhere?
Sort of like a Cuk, but swapping the capacitor and switch. Could be used for low ripple buck (drop D1 and Q2), a kind of extended-winding boost (change D1 to transistor, Q2 to diode, drop Q1 and D2), equalizing source/load (note that switching Q1+Q2 is a I/III quadrant operation), generating a negative rail (set one supply to zero, and move the diodes to a new negative rail), etc.
Tim