Highly charged states created through multiple ionization of gases are shown to enhance terahertz (THz) generation by intense, single- or two-color femtosecond laser pulses. A one-dimensional, nonpropagating fluid model reveals the main conversion processes up to ${10}^{17}\phantom{\rule{0.28em}{0ex}}\mathrm{W}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$ laser intensities, namely, ionization-induced photocurrents and plasma current oscillations. For increasing intensities, we demonstrate a cyclic growth in the THz signal associated with the different binding energies of argon and helium. This behavior is confirmed by direct particle-in-cell and unidirectional pulse propagation simulations. Changes in the forward and backward THz spectra owing to multiple ionization are discussed.