Previous work on light verb constructions (e.g. chorii kar ‘theft do; steal’) in Hindi describes their syntactic formation via co-predication (Ahmed et al., 2012, Butt, 2014). This implies that both noun and light verb contribute their arguments, and these overlapping argument structures must be composed in the syntax. In this paper, we present a co-predication analysis using Tree-Adjoining Grammar, which models syntactic composition and semantic selectional preferences without transformations (deletion or argument identification). The analysis has two key components (i) an underspecified category for the nominal and (ii) combinatorial constraints on the noun and light verb to specify selectional preferences. The former has the advantage of syntactic composition without argument identification and the latter prevents over-generalization, while recognizing the semantic contribution of both predicates. This work additionally accounts for the agreement facts for the Hindi LVC.