  We design an efficient and balanced approach that captures major effects of
collective electronic fluctuations in strongly correlated fermionic systems
using a simple diagrammatic expansion on a basis of dynamical mean-field
theory. For this aim we perform a partial bosonization of collective fermionic
fluctuations in leading channels of instability. We show that a simultaneous
account for different bosonic channels can be done in a consistent way that
allows to avoid the famous Fierz ambiguity problem. The present method
significantly improves a description of an effective screened interaction $W$
in both, charge and spin channels, and has a great potential for application to
realistic $GW$-like calculations for magnetic materials.
