Multiferroic BiFeO₃ (BFO) shows several phonon modes at infrared (IR) to THz energies, which are expected to carry information on any sample property coupled to crystal lattice vibrations. While macroscopic IR studies of BFO are often limited by single-crystal size, scattering-type scanning near-field optical microscopy (s-SNOM) allows for IR thin film spectroscopy of nanoscopic probing volumes with negligible direct substrate contribution to the optical signal. In fact, polaritons such as phonon polaritons of BFO introduce a resonant tip-sample coupling in s-SNOM, leading to both stronger signals and enhanced sensitivity to local material properties. Here, we explore the near-field response of BFO thin films at three consecutive resonances (centered around 5 THz, 13 THz, and 16 THz), by combining s-SNOM with a free-electron laser. We study the dependence of these near-field resonances on both the wavelength and tip-sample distance. Enabled by the broad spectral range of the measurement, we probe phonon modes connected to the predominant motion of either the bismuth or oxygen ions. Therefore, we propose s-SNOM at multiple near-field resonances as a versatile and very sensitive tool for the simultaneous investigation of various sample properties.