This paper investigates the theoretical capability of near-infrared spectroscopy (NIRS) systems to accurately measure changes in the oxidation state of cerebral cytochrome-c-oxidase (CCO) alongside the hemoglobins, for a deeper understanding of NIRS limitations. Concentration changes of oxy and deoxyhemoglobin (HbO and HbR) indicate the oxygen status of blood vessels and correlate with several other physiological parameters across different pathologies. The oxidation state of CCO indicates cellular energy usage efficiency through oxidative metabolism, potentially serving as a biomarker for brain and other tissue disorders. This study employs an analytical model based on the diffusion equation and statistical analyses to explore the dependency of estimated concentration changes on various systematic parameters, such as choice of wavelengths, spectral bandwidth, and uncertainties in extinction coefficient (ε) and differential pathlength factor (DPF). When there is a 10% uncertainty in DPF and ε, errors were found to be highly dependent on the number of discrete wavelengths, but not on their bandwidth if appropriate considerations are taken to account for it.