Context. Pressure profiles are sensitive probes of the thermodynamic conditions and the internal structure of galaxy clusters. The intra-cluster gas resides in hydrostatic equilibrium within the dark-matter gravitational potential. However, this equilibrium may be perturbed; for example, as a consequence of thermal energy losses, feedback, and non-thermal pressure supports. Accurate measures of the gas pressure over cosmic time are crucial for constraining cluster evolution as well as the contributions from astrophysical processes. Aims. In this work we present a novel algorithm for deriving the pressure profiles of galaxy clusters from the Sunyaev-Zeldovich (SZ) signal measured on a combination of Planck and South Pole Telescope (SPT) observations. The synergy of the two instruments makes it possible to track the profiles on a wide range of spatial scales. We exploited the sensitivity of the Planck High-Frequency Instrument to the larger scales in order to observe the faint peripheries, and took advantage of the higher spatial resolution of SPT to solve the innermost regions. Methods. We developed a two-step pipeline to take advantage of the specifications of each instrument. We first performed a component separation on the two data sets separately in order to remove the background (CMB) and foreground (Galactic emission) contaminants. We then jointly fitted a parametric pressure profile model on a combination of Planck and SPT data. Results. We validated our technique on a sample of six CHEX-MATE clusters detected by SPT. We compare the results of the SZ analysis with profiles derived from X-ray observations with XMM-Newton. We find excellent agreement between these two independent probes of the gas pressure structure.