We introduce a new class of partially coherent vortex beams in which the angular momentum
of the beam is provided from two different sources: the underlying vortex of the random
beam and the "twist" given to the ensemble of beams. The statistical and propagation
properties of such beams are investigated, and their orbital angular momentum properties
are analyzed. The combination of distinct orbital angular momentum sources allows
unusual behaviors that were previously unobserved. (C) 2018 Optical Society of America.