Experiments have shown that DNA can be sequenced using an electrolytic cell with a nanopore and an exonuclease enzyme in the cis chamber that cleaves the leading mononucleotide in a strand of DNA. The base therein can be identified with an accuracy of 80-90% by the level of the current blockade caused in the pore; a biological adapter inside slows down the cleaved mononucleotide and lowers the detection bandwidth required. In this approach, which has been mathematically modeled, analyzed, and simulated, mononucleotides are likely to be lost to diffusion or enter the pore out of order. To remedy this, a modified cell with three stacked nanopores (named UNP, MNP, and DNP) and the enzyme attached to the trans side of UNP is proposed and modeled. Mononucleotide translocation is simulated with the random walk of a dimensionless particle; the results show that the cleaved mononucleotides translocate through MNP and DNP in sequence order without loss. If this holds in practice then with a suitably designed adapter and compatible enzyme turnover rates sequencing accuracy would be limited only by the accuracy of mononucleotide discrimination. Potential implementation issues are discussed.