We present resistivity measurements of bilayer and trilayer films with layer-dependent Rashba spin-orbit interactions. A sharp upturn is observed in the temperature dependence of the parallel upper critical field. We show that it corresponds to a transition from a complex-stripe phase to a helical phase. Moreover, we propose the phase diagram of a multilayer system, which is obtained from experimental observations with the support of numerical calculations. These results pave the way for the clarification of non-trivial superconducting states in multilayer systems composed of two-dimensional Rashba superconductors.