  We present a construction of the most general BPS black holes of STU
supergravity (${\cal N}=2$ supersymmetric $D=4$ supergravity coupled to three
vector super-multiplets) with arbitrary asymptotic values of the scalar fields.
These solutions are obtained by acting with a subset of of the global symmetry
generators on STU BPS black holes with zero values of the asymptotic scalars,
both in the U-duality and the heterotic frame. The solutions are parameterized
by fourteen parameters: four electric and four magnetic charges, and the
asymptotic values of the six scalar fields. We also present BPS black hole
solutions of a consistently truncated STU supergravity, which are parameterized
by two electric and two magnetic charges and two scalar fields. These latter
solutions are significantly simplified, and are very suitable for further
explicit studies. We also explore a conformal inversion symmetry of the
Couch-Torrence type, which maps any member of the fourteen-parameter family of
BPS black holes to another member of the family. Furthermore, these solutions
are expected to be valuable in the studies of various swampland conjectures in
the moduli space of string compactifications.
