In contrast to mono- or biallelic loss of tumor-suppressor function, effects of discrete gene dysregulations, as caused by non-coding (epi)genome alterations, are poorly understood. Here, by perturbing the regulatory genome in mice, we uncover pervasive roles of subtle gene expression variation in cancer evolution. Genome-wide screens characterizing 1,450 tumors revealed that such quasi-insufficiency is extensive across entities and displays diverse context dependencies, such as distinct cell-of-origin associations in T-ALL subtypes. We compile catalogs of non-coding regions linked to quasi-insufficiency, show their enrichment with human cancer risk variants, and provide functional insights by engineering regulatory alterations in mice. As such, kilo-/megabase deletions in a Bcl11b-linked non-coding region triggered aggressive malignancies, with allele-specific tumor spectra reflecting gradual gene dysregulations through modular and cell-type-specific enhancer activities. Our study constitutes a first survey toward a systems-level understanding of quasi-insufficiency in cancer and gives multifaceted insights into tumor evolution and the tissue-specific effects of non-coding mutations.