SNPs associated with disease susceptibility often reside in enhancer clusters, or super-enhancers. Constituents of these enhancer clusters cooperate to regulate target genes and often extend beyond the linkage disequilibrium (LD) blocks containing risk SNPs identified in genome-wide association studies (GWAS). We identified 'outside variants', defined as SNPs in weak LD with GWAS risk SNPs that physically interact with risk SNPs as part of a target gene's regulatory circuitry. These outside variants further explain variation in target gene expression beyond that explained by GWAS-associated SNPs. Additionally, the clinical risk associated with GWAS SNPs is considerably modified by the genotype of outside variants. Collectively, these findings suggest a potential model in which outside variants and GWAS SNPs that physically interact in 3D chromatin collude to influence target transcript levels as well as clinical risk. This model offers an additional hypothesis for the source of missing heritability for complex traits.