We discuss the potential of the Sudbury Neutrino Observatory (SNO) to constrain the four-neutrino mixing schemes favored by the results of all neutrino oscillations experiments. These schemes allow simultaneous transitions of solar ${\ensuremath{\nu}}_{e}$'s into active ${\ensuremath{\nu}}_{\ensuremath{\mu}}$'s, ${\ensuremath{\nu}}_{\ensuremath{\tau}}$'s, and sterile ${\ensuremath{\nu}}_{s}$ controlled by the additional parameter ${\mathrm{cos}}^{2}({\ensuremath{\vartheta}}_{23}){\mathrm{cos}}^{2}({\ensuremath{\vartheta}}_{24})$ and they contain as limiting cases the pure ${\ensuremath{\nu}}_{e}$-active and ${\ensuremath{\nu}}_{e}$-sterile neutrino oscillations. We first obtain the solutions allowed by the existing data in the framework of the BBP00 standard solar model and quantify the corresponding predictions for the charged current and the neutral current to charged current (NC/CC) event ratios at SNO in the different allowed regions as a function of the active-sterile admixture. Our results show that some information on the value of ${\mathrm{cos}}^{2}({\ensuremath{\vartheta}}_{23}){\mathrm{cos}}^{2}({\ensuremath{\vartheta}}_{24})$ can be obtained by the first SNO measurement of the CC ratio, while considerable improvement on the knowledge of this mixing will be achievable after the measurement of the NC/CC ratio.