<abstract><p>In this paper, we define the $ ij $-almost-set Menger ($ ij $-ASM) property in bitopological spaces. We put up some equivalences of $ ij $-almost-set Menger bitopological spaces and investigate the behaviours of such spaces under some different types of mappings. We later take the preservation of these properties under union, subspaces, products into consideration and give some related examples. We finally introduce the concept of $ ij $-almost $ P_{\gamma} $-set in bitopological spaces.</p></abstract>