MaxNVM is a principled co-design of sparse encodings, protective logic, and fault-prone MLC eNVM technologies (i.e., RRAM and CTT) to enable highly-efficient DNN inference. We find bit reduction techniques (e.g., clustering and sparse compression) increase weight vulnerability to faults. This limits the capabilities of MLC eNVM. To circumvent this limitation, we improve storage density (i.e., bits-per-cell) with minimal overhead using protective logic. Tradeoffs between density and reliability result in a rich design space. We show that by balancing these techniques, the weights of large networks are able to reasonably fit on-chip.