  We present a general frame to extend functional renormalization group (fRG)
based computational schemes by using an exactly solvable interacting reference
problem as starting point for the RG flow. The systematic expansion around this
solution accounts for a non-perturbative inclusion of correlations. Introducing
auxiliary fermionic fields by means of a Hubbard-Stratonovich transformation,
we derive the flow equations for the auxiliary fields and determine the
relation to the conventional weak-coupling truncation of the hierarchy of flow
equations. As a specific example we consider the dynamical mean-field theory
(DMFT) solution as reference system, and discuss the relation to the recently
introduced DMF$^2$RG and the dual-fermion formalism.
