RV data from HARPS (blue dots) and NIRPS measurements. The NIRPS data is separated in unaffected datapoints (orange dots) and affected datapoints (red triangles) by the crossing of the V_syst and BERV velocities during the observations. Yellow dots are NIRPS data with the correction explained in Sect. 5.2.2. The dotted red line together with the right y axis represent the total velocity of TOI-756, showing the crossing of the BERV with the V_syst. The complete inferred model in Sect. 5.2.3, which comprises signals from the two planets along with the linear model for the acceleration (in gray), is represented by a black solid line.