Cebik W4RNL had several articles on beams based on the Bobtail Curtain and the Half-Square. Generally they
used parasitic elements of similar shape, though you could use a half-wave reflector behind each driven element.
I don't remember how much gain he got from it offhand.
I've made some computer models for 2m antennas, but the complexity generally overcomes any improvement
in gain or pattern over something like a 3-element quad.
So, yes, it can be done, but whether or not it is worthwhile depends on your needs, any other available options,
and the local ground conductivity.