Active frequency stabilization of a laser to an atomic or molecular resonance underpins many modern-day AMO physics experiments. With a flat background and high signal-to-noise ratio, modulation transfer spectroscopy (MTS) offers an accurate and stable method for laser locking. However, despite its benefits, the four-wave mixing process that is inherent to the MTS technique entails that the strongest modulation transfer signals are only observed for closed transitions, excluding MTS from numerous applications. Here we report for the first time, to the best of our knowledge, the observation of a magnetically tunable MTS error signal. Using a simple two-magnet arrangement, we show that the error signal for the Rb87F=2→F'=3 cooling transition can be Zeeman-shifted over a range of >15 GHzto any arbitrary point on the rubidium D2 spectrum. Modulation transfer signals for locking to the Rb87F=1→F'=2 repumping transition, as well as 1 GHz red-detuned to the cooling transition, are presented to demonstrate the versatility of this technique, which can readily be extended to the locking of Raman and lattice lasers.