  Let $T$ be a locally finite tree all of whose vertices have valency at least
$6$. We classify, up to isomorphism, the closed subgroups of $\mathrm{Aut}(T)$
acting $2$-transitively on the set of ends of $T$ and whose local action at
each vertex contains the alternating group. The outcome of the classification
for a fixed tree $T$ is a countable family of groups, all containing two
remarkable subgroups: a simple subgroup of index $\leq 8$ and (the semiregular
analog of) the universal locally alternating group of Burger-Mozes (with
possibly infinite index). We also provide an explicit example showing that the
statement of this classification fails for trees of smaller degree.
