Given a sparse splitting wavelength division multiplexing (WDM) network and a set of available wavelengths, we investigate the problem of provisioning a set of multicast requests simultaneously with the objective of minimizing the blocking probability. Two blocking models are taken into account: full blocking probability and partial blocking probability. As the problem is NP-hard, we propose an integer linear programming (ILP) formulation with two variants (each for a blocking model) to search for the optimal solution and several efficient adaptive heuristic algorithms to compute approximated solutions. In particular, instead of using light-trees, both ILP and heuristics use light-hierarchy, a recently proposed optimal route under sparse splitting configurations. Extensive simulations reveal that our adaptive algorithms are able to compute near-optimal solutions, and they outperform static approaches under both blocking probability models. The results also show that it is more advantageous to provision multiple multicast communications with light-hierarchies, since they are able to accommodate more requests and destinations compared to the light-tree solutions.