Single-photon multiple photoionization results from electron correlations that make this process possible beyond the independent electron approximation. To study this phenomenon experimentally, the detection in coincidence of all emitted electrons is the most direct approach. It provides the relative contribution of all possible multiple ionization processes, the energy distribution between electrons that can reveal simultaneous or sequential mechanisms, and, if possible, the angular correlations between electrons. In the present work, we present a new magnet design of our magnetic bottle electron spectrometer that allows the detection of multiply charged Xen+ ions in coincidence with n electrons. This new coincidence detection allows more efficient extraction of minor channels that are otherwise masked by random coincidences. The proof of principle is provided for xenon triple ionization.