  We derive gauge invariant operators entering definitions of the Transverse
Momentum Dependent (TMD) gluon distributions, for all five and six parton
processes. Our calculations utilize color decomposition of amplitudes in the
color flow basis. In addition, we find the general result for multi-gluon
process (with arbitrary number of gluons) at large $N_{c}$. On phenomenological
ground our results may be used for multi-jet production in the small-$x$
regime, where the TMD gluon distributions can be derived from the Color Glass
Condensate effective theory.
