  The gravitational self-force has thus far been formulated in background
spacetimes for which the metric is a solution to the Einstein field equations
in vacuum. While this formulation is sufficient to describe the motion of a
small object around a black hole, other applications require a more general
formulation that allows for a nonvacuum background spacetime. We provide a
foundation for such extensions, and carry out a concrete formulation of the
gravitational self-force in two specific cases. In the first we consider a
particle of mass $m$ and scalar charge $q$ moving in a background spacetime
that contains a background scalar field. In the second we consider a particle
of mass $m$ and electric charge $e$ moving in an electrovac spacetime. The
self-force incorporates all couplings between the gravitational perturbations
and those of the scalar or electromagnetic fields. It is expressed as a sum of
local terms involving tensors defined in the background spacetime and evaluated
at the current position of the particle, as well as tail integrals that depend
on the past history of the particle. Because such an expression is rarely a
useful starting point for an explicit evaluation of the self-force, we also
provide covariant expressions for the singular potentials, expressed as local
expansions near the world line; these can be involved in the construction of
effective extended sources for the regular potentials, or in the computation of
regularization parameters when the self-force is computed as a sum over
spherical-harmonic modes.
