The 16p11.2 and 22q11.2 copy number variants (CNVs) are associated with neurobehavioral traits including autism spectrum disorder (ASD), schizophrenia, bipolar disorder, obesity, and intellectual disability. Identifying specific genes contributing to each disorder and dissecting the architecture of CNV-trait association has been difficult, inspiring hypotheses of more complex models, such as multiple genes acting together. Using multi-tissue data from the GTEx consortium, we generated pairwise expression imputation models for CNV genes and then applied these elastic net models to GWAS for: ASD, bipolar disorder, schizophrenia, BMI (obesity), and IQ (intellectual disability). We compared the variance in these five traits explained by gene pairs with the variance explained by single genes and by traditional interaction models. We also modeled polygene region-wide effects using summed predicted expression ranks across many genes to create a regionwide score. We found that in all CNV-trait pairs except for bipolar disorder at 22q11.2, pairwise effects explain more variance than single genes. Pairwise model superiority was specific to the CNV region for all 16p11.2 traits and ASD at 22q11.2. We identified novel individual genes over-represented in top pairs that did not show single-gene signal. We also found that BMI and IQ have significant regionwide association with both CNV regions. Overall, we observe that genetic architecture differs by trait and region, but 9/10 CNV-trait combinations demonstrate evidence for multigene contribution, and for most of these, the importance of combinatorial models appears unique to CNV regions. Our results suggest that mechanistic insights for CNV pathology may require combinational models.