We study the resistive switching (RS) mechanism as a way to obtain multilevel cell (MLC) memory devices. In an MLC, more than 1 b 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-b 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 nonvolatile memory devices may compete with currently available MLCs.