The Overhauser effect in paramagnetic ions is studied theoretically for arbitrary values of electron and nuclear spins. The nuclear magnetic resonance enhancement and the degree of nuclear polarization are computed in the high-temperature approximation. The results show the possibility of obtaining simultaneous and enhanced NMR at more than one characteristic detection frequency when the hyperfine interaction is dominating. The NMR enhancement and nuclear polarization are found to be independent of the electron spin, indicating the suitability of samples with S > 12 for dynamic nuclear orientation.