  We explore how far one can go in constructing $d$-dimensional static black
holes coupled to $p$-form and scalar fields before actually specifying the
gravity and electrodynamics theory one wants to solve. At the same time, we
study to what extent one can enlarge the space of black hole solutions by
allowing for horizon geometries more general than spaces of constant curvature.
We prove that a generalized Schwarzschild-like ansatz with an arbitrary
isotropy-irreducible homogeneous base space (IHS) provides an answer to both
questions, up to naturally adapting the gauge fields to the spacetime geometry.
In particular, an IHS-K\"ahler base space enables one to construct magnetic and
dyonic 2-form solutions in a large class of theories, including non-minimally
couplings. We exemplify our results by constructing simple solutions to
particular theories such as $R^2$, Gauss-Bonnet and (a sector of)
Einstein-Horndeski gravity coupled to certain $p$-form and conformally
invariant electrodynamics.
