We explore different resistance states of metal (Ag, Ti) - manganite (La_0.325Pr_0.300Ca_0.375MnO₃) interfaces as prototypes for non-volatile memristive memory devices. In addition to High and Low resistance states accessible through bipolar pulsing with a single pulse, higher (lower) resistance states can be obtained by repeatedly applying Reset (Set) pulses. This accumulative action drives the resistance towards saturation. Our experiments reveal that the pulsing amplitude and the number of applied pulses necessary to reach a predefined target High resistance value have an exponential relationship. Simulations using a phenomenological approach (drift of oxygen vacancies induced by local electric field) confirm obtained results and provide the vacancies profiles associated to these states. Applying several Reset pulses followed by a single Set stimulus, a “pump and release” scenario is described and analyzed in terms of the local electric field developed at the interface. While sudden effects (i.e. release) can only be produced in the presence of a strong local electric field, a gradual process (i.e. pumping and accumulation) is necessary to built it up. By varying the Set amplitude we explore the dependences of the abrupt releasing process. A power law R = (I - I_thr)^p is obtained for the response-stimulus dependence, where I_thr is the threshold “cohercive amplitude” for the Set switching. This value is in agreement with the cohercive amplitude obtained by performing major and minor Hysteresis Switching Loops. Based on these findings we propose a pulsing strategy to enhance the performance of existing memristive devices.