We investigate, using series expansion techniques, the effects of higher-body local interactions in softcore lattice bosons and find that there is a systematic procedure to exactly renormalize the two-body interactions at every perturbative order; this is found to be applicable to quantum critical as well as ground state properties within the Mott insulating lobe.  Preliminary work on finite temperature effects in interacting hardcore bosons (XXZ-type spin models) will be briefly mentioned.