We discuss the consequences of relaxing the Minimal Flavour Violation assumption in the up-squark sector for the mass of the lightest Higgs scalar and we derive the approximate analytical formulae that quantify this effect. We show that $m_h$ can be enhanced by up to $13-14$ GeV in the case of the phenomenological MSSM with the inverted hierarchy of masses in the squark sector and zero stop mixing, and up to $4-5$ GeV in GUT-constrained scenarios where the magnitude of the enhancement is mitigated by renormalization group effects. We also confront the scenarios allowing for the Higgs mass enhancement with the experimental constraints on the off-diagonal SSB entries coming from the FCNC processes.