\noindent In this paper, we show that for any positive integers $r$, $k$, $Θ$, and $Γ$ such that $k \geq 2$ and $r \geq k + Γ$, there exists a connected graph $G$ for which $$\begin{array}{llcr} ω(G) = χ(G) = k, & χ\left( G , rK_2 \right) = Θ, & {\rm and} & |E(G)| - {\rm ex}\left( G , rK_2 \right) = Θ+ Γ. \end{array}$$
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