We report on non-volatile memory devices based on multifunctional manganites. The electric field induced resistive switching of Ti/La_1/3Ca_2/3MnO₃/n -Si devices is explored using different measurement protocols. We show that using current as the electrical stimulus (instead of standard voltage-controlled protocols) improves the electrical performance of our devices and unveils an intermediate resistance state. We observe three discrete resistance levels (low, intermediate and high), which can be set either by the application of current-voltage ramps or by means of single pulses. These states exhibit retention and endurance capabilities exceeding 10⁴s and 70 cycles, respectively. We rationalize our experimental observations by proposing a mixed scenario were a metallic filament and a SiO_x layer coexist, accounting for the observed resistive switching. Overall electrode area dependence and temperature dependent resistance measurements support our scenario. After device failure takes place, the system can be turned functional again by heating up to low temperature (120°C), a feature that could be exploited for the design of memristive devices with self-healing functionality. These results give insight into the existence of multiple resistive switching mechanisms in manganite-based memristive systems and provide strategies for controlling them.