  Based on earlier work of the third author, we construct a Chang-type model
with supercompact measures extending a derived model of a given hod mouse with
a regular cardinal $\delta$ that is both a limit of Woodin cardinals and a
limit of ${<}\delta$-strong cardinals. The existence of such a hod mouse is
consistent relative to a Woodin cardinal that is a limit of Woodin cardinals.
We argue that our Chang-type model satisfies $\mathsf{AD}^+ +
\mathsf{AD}_{\mathbb{R}} + \Theta$ is regular + $\omega_1$ is
${<}\delta_{\infty}$-supercompact for some regular cardinal
$\delta_{\infty}>\Theta$. This complements Woodin's generalized Chang model,
which satisfies $\mathsf{AD}^+ + \mathsf{AD}_{\mathbb{R}}+\omega_1$ is
supercompact, assuming a proper class of Woodin cardinals that are limits of
Woodin cardinals.
