Finite simple groups in which all maximal subgroups are $\pi$-closed. II

We continue the study of pairs $(G,\pi)$, where $G$ is a finite simple nonabelian group and $\pi$ a set of primes, such that $G$ has only $\pi$-closed maximal subgroups but is not $\pi$-closed itself. Using the results of the first paper from the series, we give a list of such pairs $(G,\pi)$ in the case when $G$ is different from the groups $PSL_r(q)$ and $PSU_r(q)$ with prime odd $r$ and $E_8(q)$, where $q$ is a prime power.