Aqueous sodium-ion batteries operating in neutral pH electrolytes offer the potential for low cost, low toxicity, high safety, and high power density energy storage for large-scale applications, such as those needed to store electricity from renewable energy sources. However, the mechanisms of ion intercalation into solid-state electrodes operating in neutral pH aqueous electrolytes are not well understood. Layered, Mn-rich sodium oxides are promising electrode materials because of the abundance and safety of manganese. Initial studies of the moisture-stable, layered P2-type oxide, Na_xNi_0.22Mn_0.66Co_0.11O₂ (NaNMC) show an irreversible phase transition to a hydrated birnessite-like structure during electrochemical cycling in aqueous electrolytes with approximately 25 mAh/g reversible capacity. This work investigates the transformation mechanism of the NaNMC through ex situ X-ray diffraction, in situ Raman spectroscopy, and ex situ transmission electron microscopy. A systematic investigation is then conducted on the effect of transition metal doping in NaNMC to reduce the amount of Ni and Co, and to tune the redox potential and capacity for electrochemical cycling in aqueous electrolytes. In addition, aqueous solutions with both high and low salt concentrations are investigated to determine the effect of the electrolyte on the electrochemical behavior of layered sodium oxides