Capacitive deionization (CDI) is a relatively novel desalination technology which uses electrically charged porous electrodes to remove ions from low salinity water streams. The interplay between the micro- and macroscale transport mechanisms in the porous electrodes and bulk flow of the CDI unit dictates the concentration profile at the exit. A thorough understanding of these interactions is important towards achieving high-efficiency systems. Through permutation of the associated transport time constants, we conduct a parametric study to investigate the coupling of multiscale phenomena in CDI. Moreover, we propose a new multi-cycle arrangement to further improve the desalination performance of a given saline solution. In these systems, the regeneration feed stream used for each cycle highly affects the efficiency of the whole system, as it directly affects the water recovery ratio, the total duration of the process, and the desalination performance of the next cycle. We propose three regeneration schemes, with different regeneration feed streams to enhance the desalination/regeneration performance of the multi-cycle arrangements. To obtain comprehensive characterization of desalination and regeneration performances of different units, we introduce new inclusive metrics that encompass different aspects of the system. The results indicate trade-offs between desalination performance and energy efficiency of the proposed arrangements.