The case of $\hat{Q}(\chi_1)\cdot\hat{Q}(\chi_1)$-$\hat{Q}(\chi_2)\cdot\hat{Q}(\chi_2)$ mixing in the interacting boson model is studied within its mean-field approximation. It is shown that the criticality conditions lead to two classes of solutions and that $\chi_1$ and $\chi_2$ need to have an opposite sign to make prolate-oblate shape coexistence possible. Phase diagrams for selected cases have been constructed.