  We generalize overpartitions to (k,j)-colored partitions: k-colored
partitions in which each part size may have at most j colors. We find numerous
congruences and other symmetries. We use a wide array of tools to prove our
theorems: generating function dissections, modular forms, bijections, and other
combinatorial maps. We find connections to divisor sums, the
Han/Nekrasov-Okounkov hook length formula and a possible approach to a
finitization, and other topics, suggesting that a rich mine of results is
available.
