Search for new multicomponent solid forms has become a key step in pharmaceutical drug development. Apremilast, a poorly soluble API used for the treatment of psoriatic arthritis, was used as a model compound in this work. There have been several isostructural cocrystals of this API already described in the literature. In this paper, a new isostructural cocrystal (with phthalic acid) and solvates (with oxylene and fluorobenzene) of the studied compound were successfully designed. Furthermore, to the best of our knowledge, this work is the first ever to prepare a non-isostructural cocrystal of apremilast with cinnamic acid. The crystal structures of all the new multicomponent forms were successfully solved using single crystal X-ray diffraction. The differences between the formation of the isostructural and nonisostructural forms are explained in detail using the structural characterization of the prepared forms and the density functional theory calculations (B3LYP/6-31G(d,p) level of theory). The physicochemical characterization complemented the structural one, including the thermal properties (differential scanning calorimetry, DSC) and the intrinsic dissolution rate (IDR). The samples were further characterized by X-ray powder diffraction (XRPD) and Raman spectroscopy. The dissolution experiments showed that the new multicomponent solids can improve the intrinsic dissolution rate by up to 500% compared to the polymorph of apremilast used in the marketed drug product.