Set of Turing machines $S$ such that any $A \in S$ halts on input the description of any $B \in S$
Let us construct a Turing machine $M$ such that $M$ first generates its own description $\langle M \rangle$ by recursion theorem. Then for any input $w$ it first checks if $w=\langle M \rangle$, if yes it halts. If not it starts counting infinitely. Now let $S=\{\langle M \rangle\}$. If you try to add any other Turing machine $T$ to $S$ , it could not be part of $S$ as $M$ won't halt on $\langle T \rangle$. Thus following your definition of a maximal set,  $S=\{\langle M \rangle\}$ is such a set.