  We consider $(k,j)$-colored partitions, partitions in which $k$ colors exist
but at most $j$ colors may be chosen per size of part. In particular these
generalize overpartitions. Advancing previous work, we find new congruences,
including in previously unexplored cases where $k$ and $j$ are not coprime, as
well as some noncongruences. As a useful aside, we give the apparently new
generating function for the number of partitions in the $N \times M$ box with a
given number of part sizes, and extend to multiple colors a conjecture of
Dousse and Kim on unimodality in overpartitions.
