  New extensions of the KP and modified KP hierarchies with self-consistent
sources are proposed. The latter provide new generalizations of
$(2+1)$-dimensional integrable equations, including the DS-III equation and the
$N$-wave problem. Furthermore, we recover a system that contains two types of
the KP equation with self-consistent sources as special cases. Darboux and
binary Darboux transformations are applied to generate solutions of the
proposed hierarchies.
