  We study certain bi-scalar-tensor theories emanating from conformal symmetry
requirements of Horndeski's four-dimensional action. The former scalar is a
Galileon with shift symmetry whereas the latter scalar is adjusted to have a
higher order conformal coupling. Employing technics from local Weyl geometry
certain Galileon higher order terms are thus constructed to be conformally
invariant. The combined shift and partial conformal symmetry of the action,
allow us to construct exact black hole solutions. The black holes initially
found are of planar horizon geometry embedded in anti de Sitter space and can
accommodate electric charge. The conformally coupled scalar comes with an
additional independent charge and it is well-defined on the horizon whereas
additional regularity of the Galileon field is achieved allowing for time
dependence. Guided by our results in adS space-time we then consider a higher
order version of the BBMB action and construct asymptotically flat, regular,
hairy black holes. The addition of the Galileon field is seen to cure the BBMB
scalar horizon singularity while allowing for the presence of primary scalar
hair seen as an independent integration constant along-side the mass of the
black hole.
