We report on the growth and characterization of Ti/La_1/3Ca_3/2MnO₃/SiO₂/n-Si memristive devices. We demonstrate that using current as electrical stimulus unveils an intermediate resistance state, in addition to the usual high and low resistance states that are observed in the standard voltage controlled experiments. Based on thorough electrical characterization (impedance spectroscopy, current-voltage curves analysis), we disclose the contribution of three different microscopic regions of the device to the transport properties: an ohmic incomplete metallic filament, a thin manganite layer below the filament tip exhibiting Poole-Frenkel like conduction, and the SiO_x layer with an electrical response well characterized by a Child-Langmuir law. Our results suggest that the existence of the SiO_x layer plays a key role in the stabilization of the intermediate resistance level, indicating that the combination of two or more active resistive switching oxides adds functionalities in relation to the single-oxide devices. We understand that these multilevel devices are interesting and promising, as their fabrication procedure is rather simple and they are fully compatible with the standard Si-based electronics.