The invention is directed to a compound comprising one or more CD1d complexes in association with an antibody specific for a cell surface marker. The CD1d complexes comprise a CD1d, a β2-microglobulin molecule, and may further comprise an antigen bound to the CD1d binding groove. The invention is further directed to methods of inhibiting or stimulating an immune response with the CD1d-antibody compounds, in particular anti-tumor and autoimmunity responses.