  We consider analogues of Grigorchuk-Gupta-Sidki (GGS-)groups acting on trees
of growing degree; the so-called growing GGS-groups. These groups are not just
infinite and do not possess the congruence subgroup property, but many of them
are branch and have the $p$-congruence subgroup property, for a prime $p$.
Among them, we find groups with maximal subgroups only of finite index, and
with infinitely many such maximal subgroups. These give the first examples of
finitely generated branch groups with infinitely many finite-index maximal
subgroups. Additionally, we prove that congruence quotients of growing
GGS-groups associated to a defining vector of zero sum give rise to Beauville
groups.
