In an $\mathrm{SU}\left(3\right)\mathrm{}$-symmetric quark model, double-charge-exchange scattering processes of the type $\mathrm{PN}\to P^{\prime }B$, $\Delta Q(P,P^{\prime })=\pm 2$, are investigated. The physical baryon octet is taken as $8 \left(\mathrm{physical}\right)=8^{\prime } cos\theta +8 sin\theta$, where 8 and 8′ arise, respectively, from $3\otimes \overline{3}$ and $3\otimes 6$ contained in $3\otimes 3\otimes 3$. In terms of the mixing angle $\theta$, a number of predictions are made.

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