Property theory is, as I have understood it, first of all characterized by an attempt to approach naive comprehension type-freely and without committing to extensionality.

There is e.g. the work of Raymond Turner in $A \ Theory \ of \ Properties$ in JSL 52(2) 1987 and his monograph $Truth \ and\ Modality\ for\ Knowledge\ Representation$ (Pitman) 1990 as well as $Semantics\ and\ Property\ Theory$ by Gennaro Chierchia and Raymond Turner in Linguistics and Philosophy, Vol. 11, No. 3 (Aug., 1988), pp. 261-302, plus works cited.

Are there any important new developments of property theory beyond the work mentioned?