We report vibrating reed and superconducting quantum interference device magnetometer data that exhibit prominent dips or oscillations of the superconducting (SC) onset temperature, ΔTC(H)≈0.01–0.7K, for a [Nb(23nm)∕Ni(5nm)]5 multilayer (ML) in dc magnetic fields applied nearly parallel to the ML plane. The vibrating reed data exhibit reproducible structures below TC that may reflect multiple SC transitions, but they are sensitive to ac field amplitude and dc field orientation. This striking behavior poses challenges for theoretical and experimental investigations of interfaces between SC and ferromagnetic layers that involve magnetic pair breaking effects, “pi phase shifts” of the SC order parameter, and exotic (“LOFF”) pairing states. Alternatively, the anomalies may mark dynamical instabilities within a confined, strongly anisotropic Abrikosov vortex lattice.