  A finite subset $X$ of the Euclidean space is called an $m$-distance set if
the number of distances between two distinct points in $X$ is equal to $m$. An
$m$-distance set $X$ is said to be maximal if any vector cannot be added to $X$
while maintaining the $m$-distance condition. We investigate a necessary and
sufficient condition for vectors to be added to a regular simplex such that the
set has only $2$ distances. We construct several $d$-dimensional maximal
$2$-distance sets that contain a $d$-dimensional regular simplex. In
particular, there exist infinitely many maximal non-spherical $2$-distance sets
that contain both the regular simplex and the representation of a strongly
resolvable design. The maximal $2$-distance set has size $2s^2(s+1)$, and the
dimension is $d=(s-1)(s+1)^2-1$, where $s$ is a prime power.
