  We develop a framework to systematically investigate the influence of
many-particle interference on the dynamics of generic $-$ possibly interacting
$-$ bosonic systems. We consider mixtures of bosons which belong to several
distinguishable species, allowing us to tune the level of many-particle
interference, and identify the corresponding signatures in the time-dependent
expectation values of observables. Interference contributions to these
expectation values can be classified based on the number of interfering
particles. Interactions are shown to generate a series of additional,
higher-order interference contributions. Finally, based on a decomposition of
the Hilbert space of partially distinguishable bosons into irreducible
representations of the unitary group, we determine some spectral
characteristics of (in)distinguishability.
