Genuine multiparticle correlations among hadrons with the same charge produced in Z decays are studied using the high statistics data collected with the OPAL detector at LEP. Normalized factorial cumulants up to fourth order are used to measure particle correlations as a function of domain size in rapidity, azimuthal angle and transverse momentum. The data are compared with the Monte Carlo model PYTHIA. The importance of short-range correlations between particles with the same charge is studied using recently proposed algorithms which simulate the effect of Bose-Einstein correlations. These algorithms reproduce reasonably well the measured second- and higher-order correlations of same-charge as well as of all-charge particle combinations.