Cooling of atomic motion is a crucial tool for many branches of atomic physics, ranging from fundamental physics explorations to quantum information and sensing. For trapped ions, electromagnetically-induced-transparency (EIT) cooling has received attention for the relative speed, low laser power requirements, and broad cooling bandwidth of the technique. However, in applications where the ion used for cooling has hyperfine structure to enable long coherence times, it is difficult to find a closed three-level system in which to perform standard EIT cooling. Here, we demonstrate successful EIT cooling on
25Mg+ by the addition of an extra laser frequency; this method can be applied to any ion with nonzero nuclear spin. Furthermore, we simultaneously EIT cool all axial modes in mixed-species crystals $^{9}\mathrm{Be}^{+}\text{\ensuremath{-}}^{25}\mathrm{Mg}^{+}$ and $^{9}\mathrm{Be}^{+}\text{\ensuremath{-}}^{25}\mathrm{Mg}^{+}\text{\ensuremath{-}}^{9}\mathrm{Be}^{+}$ through the
25Mg+ ion. This demonstrates the viability of EIT cooling in architectures where the laser-cooled species can host high-fidelity hyperfine qubits.