  We characterize the class of exchangeable Feller processes evolving on
partitions with boundedly many blocks. In continuous-time, the jump measure
decomposes into two parts: a $\sigma$-finite measure on stochastic matrices and
a collection of nonnegative real constants. This decomposition prompts a
L\'evy-It\^o representation. In discrete-time, the evolution is described more
simply by a product of independent, identically distributed random matrices.
