  We discuss different approximations for effective low-energy interactions in
multi-band models for weakly correlated electrons. In the study of Fermi
surface instabilities of the conduction band(s), the standard approximation
consists only keeping those terms in the bare interactions that couple only to
the conduction band(s), while corrections due to virtual excitations into bands
away from the Fermi surface are typically neglected. Here, using a functional
renormalization group approach, we present an improved truncation for the
treatment of the effective interactions in the conduction band that keeps track
of the generated three-particle interactions (six-point term) and hence allows
one to include important aspects of these virtual interband excitations. Within
a simplified two-patch treatment of the conduction band, we demonstrate that
these corrections can have a rather strong effect in parts of the phase diagram
by changing the critical scales for various orderings and the phase boundaries.
