The effect of various amphiphilic block copolymers of different molar masses on the structure and phase behavior of ternary amphiphilic systems (water, oil, and nonionic surfactant) is investigated. Small amounts of PEP-PEO block copolymer lead to a dramatic increase in the volumes of oil and water, which can be solubilized in a bicontinuous microemulsion. High-precision neutron scattering experiments with a sophisticated contrast variation technique demonstrate that the polymers form uniformly distributed mushroom conformations on the surfactant membrane. Based on these observations, we propose a universal mechanism for the swelling behavior, which is due to the variation of the membrane curvature elasticity.