  We present the $CWR$ invariant, a new invariant for alternating links, which
builds upon and generalizes the $WRP$ invariant. The $CWR$ invariant is an
array of two-variable polynomials that provides a stronger invariant compared
to the $WRP$ invariant. We compare the strength of our invariant with the
classical HOMFLYPT, Kauffman $3$-variable, and Kauffman $2$-variable
polynomials on specific knot examples. Additionally, we derive general
recursive "skein" relations, and also specific formulas for the initial
components of the $CWR$ invariant using weighted adjacency matrices of modified
Tait graphs.
