The electrophoresis of a charge-regulated particle is modeled under the conditions where the dispersion medium contains multiple ionic species and the influence of a boundary can be significant. The conditions assumed in this study are much closer to reality than those of the available analyses in the literature, and, therefore, the results gathered provide valuable information to both theoreticians and experimentalists. For illustration, we consider the electrophoresis of a sphere in a cylindrical pore filled with four kinds of ionic species, namely, H+, OH-, Na+, and Cl-; these ions are usually present in experiments where the bulk pH is adjusted by HCl and NaOH. We show that the presence of the pore has the effect of inhibiting the polarization of the double layer near a particle, thereby influencing both quantitatively and qualitatively the electrophoretic behavior of the particle. If the pore is charged, then the effect of electroosmotic flow needs be considered, yielding interesting phenomena that might play a key role in practice.