The extent to which the impact of regulatory genetic variants may depend on other factors, such as the expression levels of upstream transcription factors, remains poorly understood. Here we report a framework in which regulatory variants are first aggregated into sets, and using these as estimates of the total cis-genetic effects on a gene we model their non-additive interactions with the expression of other genes in the genome. Using 1220 lymphoblastoid cell lines across platforms and independent datasets we identify 74 genes where the impact of their regulatory variant-set is linked to the expression levels of networks of distal genes. We show that these networks are predominantly associated with tumourigenesis pathways, through which immortalised cells are able to rapidly proliferate. We consequently present an approach to define gene interaction networks underlying important cellular pathways such as cell immortalisation.