  The purpose of this paper is to construct new families of irreducible
Gelfand-Tsetlin modules for U_q(gl_n). These modules have arbitrary singularity
and Gelfand-Tsetlin multiplicities bounded by 2. Most previously known
irreducible modules had all Gelfand-Tsetlin multiplicities bounded by 1
\cite{FRZ1}, \cite{FRZ2}. In particular, our method works for q=1 providing new
families of irreducible Gelfand-Tsetlin modules for gl_n. This generalizes the
results of \cite{FGR3} and \cite{FRZ}.
