Under squeezing flow, magnetorheological fluid can undergo a strengthening phenomenon which results in a drastic increase of its yield stress. This behavior, also known as the super-strong effect, could be used to significantly increase the performance (e.g. torque-to-weight) of rotary magnetorheological fluid devices (e.g. brakes, clutches), but has yet to be exploited due to limited predictability of the phenomenon. To better understand the occurrence of the super-strong effect, a novel test bench capable of small amplitude oscillatory shear is designed to study the behavior of highconcentration magnetorheological fluid submitted to different simultaneous squeeze-shear conditions and magnetic field strengths. Experimental results, obtained up to 5 mm/s compression speed, show that the squeeze-strengthening effect can be correlated to the Péclet number when squeeze flow is dominant, suggesting that the super-strong behavior is governed by solid-liquid phase separation. This super-strong effect, however, is found greatly reduced when the superimposed shear-rate approaches the squeeze-rate order of magnitude.