Tissue engineering and stem cell research greatly benefit from cell encapsulation within hydrogels as it promotes cell expansion and differentiation. Affinity-triggered hydrogels, an appealing solution for mild cell encapsulation, rely on selective interactions between the ligand and target and also on the multivalent presentation of these two components. Although these hydrogels represent a versatile option to generate dynamic, tunable, and highly functional materials, the design of hydrogel properties based on affinity and multivalency remains challenging and unstudied. Here, the avidin-biotin affinity pair, with the highest reported affinity constant, is used to address this challenge. It is demonstrated that the binding between the affinity hydrogel components is influenced by the multivalent display selected. In addition, the natural multivalency of the interaction must be obeyed to yield robust multicomponent synthetic protein hydrogels. The hydrogel's resistance to erosion depends on the right stoichiometric match between the hydrogel components. The developed affinity-triggered hydrogels are biocompatible and support encapsulation of induced pluripotent stem cells and their successful differentiation into a neural cell line. This principle can be generalized to other affinity pairs using multimeric proteins, yielding biomaterials with controlled performance.