  Parisi-Sourlas (PS) supersymmetry is known to emerge in some models with
random field type of disorder. When PS SUSY is present the $d$-dimensional
theory allows for a $d-2$-dimensional description. In this paper we investigate
the reversed question and we provide new indications that any given CFT$_{d-2}$
can be uplifted to a PS SUSY CFT$_{d}$. We show that any scalar four-point
function of a CFT$_{d-2}$ is mapped to a set of 43 four-point functions of the
uplifted CFT$_{d}$ which are related to each other by SUSY and satisfy all
necessary bootstrap axioms. As a byproduct we find 43 non trivial relations
between conformal blocks across dimensions.
  We test the uplift in generalized free field theory (GFF) and find that PS
SUSY is a powerful tool to bootstrap an infinite class of previously unknown
GFF observables. Some of this power is shown to persist in perturbation theory
around GFF.
  We explain why all diagonal minimal models admit an uplift and we show exact
results for correlators and CFT data of the $4d$ uplift of the Ising model.
Despite being strongly coupled $4d$ CFTs, the uplifted minimal models contain
infinitely many conserved currents and are expected to be integrable.
