The current data of the LHC disfavours light masses for first and
second generation squarks. This presents a problem for models with a
Minimal Flavour Violation structure, where such bounds constrain how
light the third generation squark masses can be, and put at risk the
solution of the Higgs hierarchy problem. As a way out, we present a
new framework based on a U(2)5 flavour symmetry, which allows the
third generation sfermion masses to be light regardless of the
constraints on the first two generations. We show how this framework
can solve flavour tensions in the quark sector. Furthermore, we
attempt to extend this framework in order to accommodate neutrino
data, and get predictions for neutrinoless double beta decay, neutrino
masses and lepton flavour violating processes.