On almost good triples of vertices in edge regular graphs

Consider a connected edge regular graph $\Gamma$ with parameters $(v,k,\lambda)$ and put $b_1=k-\lambda-1$. A triple $(u,w,z)$ of vertices is called (almost) good whenever $d(u,w)=d(u,z)=2$ and $\mu(u,w)+\mu(u,z)\le2k-4b_1+3$ (and $\mu(u,w)+\mu(u,z)=2k-4b_1+4$). If $k=3b_1+\gamma$ with $\gamma\ge-2$, a triple $(u,w,z)$ is almost good, and $\Delta=[u]\cap[w]\cap[z]$then: either $|\Delta|\le2$; or $\Delta$ is a 3-clique and $\Gamma$ is a Clebsch graph; or $\Delta$ is a 3-clique, $k=16$, $b_1=6$ and $v=31$; or $\Delta$ is a 4-clique and $\Gamma$ is a Schläfli graph.