Physical properties of selected members of R₂T₂X family of intermetallic compounds will be presented, especially with respect to the pressure tuning of their transport, magnetic and structural properties. In particular, pressure-driven suppression of Ce₂Pd₂In magnetism will be discussed with respect to the pressure-induced structural changes observed via high-pressure X-ray diffraction experiment. The second system is non-magnetic analogue La₂Pd₂In studied at extreme conditions to estimate the lattice related contributions to observed behavior exhibiting the BCS superconductivity below 1.4 K. Last but not least, magnetic properties of R₂Cu₂In compounds with R = Dy, Tm and Lu from the “localized” part of R₂T₂X story (non-magnetic --> localized --> complex) were studied. Tm₂Cu₂In lying at the border of crystal structure stability was found to exhibit the glassy features with pressure dependence, which can be interpreted as the consequence of enhancement of spin dynamics in elevated pressures.