We study the resistive switching (RS) mechanism as way to obtain multi-level memory cell (MLC) devices. In a MLC more than one bit of information can be stored in each cell. Here we identify one of the main conceptual difficulties that prevented the implementation of RS-based MLCs. We present a method to overcome these difficulties and to implement a 6-bit MLC device with a manganite-based RS device. This is done by precisely setting the remnant resistance of the RS-device to an arbitrary value. Our MLC system demonstrates that transition metal oxide non-volatile memories may compete with the currently available MLCs.