Multi-write coding of non-volatile memories including a method that receives write data, and a write address of a memory page. The memory page is in either an erased state or a previously written state. If the memory page is in the erased state: selecting a first codeword from a code such that the first codeword encodes the write data and is consistent with a target set of distributions of electrical charge levels in the memory page; and writing the first codeword to the memory page. If the memory page is in the previously written state: selecting a coset from a linear code such that the coset encodes the write data and includes one or more words that are consistent with previously written content of the memory page; selecting a subsequent codeword from the one or more words in the coset; and writing the subsequent codeword to the memory page.