Although rare genetic conditions are mostly caused by DNA sequence alterations that functionally disrupt individual genes, large-scale studies using genome sequencing have started to unmask additional complexity. Understanding how combinations of variants in different genes shape human phenotypes is expected to provide important insights into the clinical and genetic heterogeneity of rare disorders. Here, we use albinism, an archetypal rare condition associated with hypopigmentation, as an exemplar for the study of genetic interactions. We analyse data from the Genomics England 100,000 Genomes Project alongside a cohort of 1120 individuals with albinism, and investigate the effect of dual heterozygosity for the combination of two established albinism-related variants: TYR:c.1205 G > A (p.Arg402Gln) [rs1126809] and OCA2:c.1327 G > A (p.Val443Ile) [rs74653330]. As each of these changes alone is insufficient to cause disease when present in the heterozygous state, we sought evidence of synergistic effects. We show that, when both variants are present, the probability of receiving a diagnosis of albinism is significantly increased (odds ratio 12.8; 95% confidence interval 6.0 – 24.7; p-value 2.1 ×10−8). Further analyses in an independent cohort, the UK Biobank, support this finding and highlight that heterozygosity for the TYR:c.1205 G > A and OCA2:c.1327 G > A variant combination is associated with statistically significant alterations in visual acuity and central retinal thickness (traits that are considered albinism endophenotypes). The approach discussed in this report opens up new avenues for the investigation of oligogenic patterns in apparently Mendelian disorders.