We extend the Kulkarni class of multivariate phase–type distributionsin a natural time–fractional way to construct a new class of multivariatedistributions with heavy-tailed Mittag-Leffler(ML)-distributed marginals.The approach relies on assigning rewards to a non–Markovian jump processwith ML sojourn times. This new class complements an earlier multivari-ate ML construction [2] and in contrast to the former also allows for taildependence. We derive properties and characterizations of this class, andwork out some special cases that lead to explicit density representations.