  A covariant scheme for material coupling with $GL(N,R)$ gauge formulation of
gravity is studied. We revisit a known idea of a Yang-Mills type construction,
where quadratical power of cosmological constant have to be considered in
consistence with vacuum Einstein's gravity. Then, matter coupling with gravity
is introduced and some constraints on fields and background appear. Finally,
exploring the N=3 case we elucidate that introduction of auxiliary fields
decreases the number of these constraints.
