  Starting from the static, spherically symmetric black hole solutions in
massless Einstein-Maxwell-dilaton (EMD) theories, we build a "skeleton" action,
that is, we phenomenologically replace black holes by an appropriate effective
point particle action, which is well suited to the formal treatment of the
many-body problem in EMD theories. We find that, depending crucially on the
value of their scalar cosmological environment, black holes can undergo steep
"scalarization" transitions, inducing large deviations to the general
relativistic two-body dynamics, as shown, for example, when computing the first
post-Keplerian Lagrangian of EMD theories.
