First two rows: TESS light curve and best-fit transit models (left panels), and spectroscopic orbits (HARPS-N DRS RVs; right panels) related to planets HD 63433 b and HD 63433 c. Here, we show the solution obtained with model M4. The upper right plot shows the RV residuals, after removing the Doppler signal due to HD 63433 c and the stellar activity term from the original data, phased to the orbital period of 7.01794 d: it appears clear that the spectroscopic orbit corresponding to HD 63433 b remains not characterised. The phase-folded plot for HD 63433 c shows the RV residuals after removing the stellar activity term from the original data. Third row: Zoomed view of the stellar activity term in the HARPS-N RVs, after removing the Doppler signal due to HD 63433 c from the original RVs, as modelled by a GP quasi-periodic kernel. In model M5, the GP quasi-periodic kernel was trained on the time series of the log chromospheric activity diagnostic.