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In this article, we investigate how the coefficient $f(z)$ affects the number of positive solutions of the quasilinear elliptic system $$displaylines{ -Delta_{p}u =lambda g(z)|u|^{q-2}u+frac{alpha}{alpha+eta} f(z)|u|^{alpha-2}u|v|^{eta} quadhbox{in }Omega,cr -Delta_{p}v =mu h(z)|v|^{q-2}v +frac{eta}{alpha+eta}f(z)|u|^{alpha}|v|^{eta-2}v quadhbox{in }Omega,cr u=v=0quadhbox{on }partialOmega, }$$ where $0inOmegasubset mathbb{R}^{N}$ is a bounded domain, $alpha >1$, $eta>1$ and $1<p<q<alpha+eta=p^{*}=frac{Np}{N-p}$ for $N>2p$.