Phase-change materials (PCMs) allow for non-volatile resonance tuning of nanophotonic components. Upon switching, they offer a large dielectric contrast between their amorphous and crystalline phases. The recently introduced “plasmonic PCM” In₃SbTe₂ (IST) additionally features in its crystalline phase a sign change of its permittivity over a broad infrared spectral range. While optical resonance switching in unpatterned IST thin films has been investigated before, nanostructured IST antennas have not been studied, yet. Here, we present numerical and experimental investigations of nanostructured IST rod and disk antennas. By crystallizing the IST with microsecond laser pulses, we switched individual antennas from narrow dielectric to broad plasmonic resonances. For the rod antennas, we demonstrated a resonance shift of up to 1.2 µm (twice the resonance width), allowing on/off switching of plasmonic resonances with a contrast ratio of 2.7. With the disk antennas, we realized an increase of the resonance width by more than 800% from 0.24 µm to 1.98 µm while keeping the resonance wavelength constant. Further, we demonstrated intermediate switching states by tuning the crystallization depth within the resonators. Our work empowers future design concepts for nanophotonic applications like active spectral filters, tunable absorbers, and switchable flat optics.