Range of masses and semi-minor axis that allows a companion to tilt the outer planets of the system while preserving its mutual inclinations. The system is not destroyed for companions below the line β_KL,ce = 1 and tilting is possible for a frequency ratio larger than 1. The companion has a significant influence on the system if its angular momentum is larger than the system’s angular momentum. Otherwise, the companion’s orbit precesses around the system angular momentum and does not induce large obliquity for the system. The green region is the 5σ limit set by direct imaging constraints. The purple and blue curve are the 5σ limit set by RVs, assuming a circular orbit and inclinations of 90 and 35°.