Syntax-based distributional models of lexical semantics provide a flexible and linguistically adequate representation of co-occurrence information. However, their construction requires large, accurately parsed corpora, which are unavailable for most languages. In this paper, we develop a number of methods to overcome this obstacle. We describe (a) a crosslingual approach that constructs a syntax-based model for a new language requiring only an English resource and a translation lexicon; and (b) multilingual approaches that combine crosslingual with monolingual information, subject to availability. We evaluate on two lexical semantic benchmarks in German and Croatian. We find that the models exhibit complementary profiles: crosslingual models yield higher accuracies while monolingual models provide better coverage. In addition, we show that simple multilingual models can successfully combine their strengths.