Reconstituted basement membrane (rBM) products like Matrigel are widely used in 3D culture models of epithelial tissues and cancer. However, their utility is hindered by key limitations, including batch variability, xenogenic contaminants, and a lack of tunability. To address these challenges, we engineered a 3D basement membrane (eBM) matrix by conjugating defined extracellular matrix (ECM) adhesion peptides (IKVAV, YIGSR, RGD) to an alginate hydrogel network with precisely tunable stiffness and viscoelasticity. We optimized the mechanical and biochemical properties of the engineered basement membranes (eBMs) to support mammary acinar morphogenesis in MCF10A cells, similar to rBM. We found that IKVAV-modified, fast-relaxing (τ1(/2) = 30-150 s), and soft (E = 200 Pa) eBMs best promoted polarized acinar structures. Clusters became invasive and lost polarity only when the IKVAV-modified eBM exhibited both similar stiffness to a malignant breast tumor (E = 4000 Pa) and slow stress relaxation (τ1(/2) = 600-1100 s). Notably, tumor-like stiffness alone was not sufficient to drive invasion in fast stress relaxing matrices modified with IKVAV. In contrast, RGD-modified matrices promoted a malignant phenotype regardless of mechanical properties. We also utilized this system to interrogate the mechanism driving acinar and tumorigenic phenotypes in response to microenvironmental parameters. A balance in activity between β1- and β4-integrins was observed in the context of IKVAV-modified eBMs, prompting further investigation into the downstream mechanisms. We found differences in hemidesmosome formation and production of endogenous laminin in response to peptide type, stress relaxation, and stiffness. We also saw that inhibiting either focal adhesion kinase or hemidesmosome signaling in IKVAV eBMs prevented acinus formation. This eBM matrix is a powerful, reductionist, xenogenic-free system, offering a robust platform for both fundamental research and translational applications in tissue engineering and disease modeling.