Major histocompatibility complex (MHC ) epitope presentation is needed for robust adaptive immune responses. Core peptide binding motifs for class I and class II MHC are 8-10 amino acids long, containing two or more "anchor" residues. These binding motifs define epitope anchor amino acid content and spacing, and knowledge of them has facilitated emergence of polyepitope vaccines. However, polyepitopes can exhibit "junctional epitopes" (neoepitopes interfering with vaccine function) resulting from juxtaposition of authentic epitopes. We have developed an algorithm for consideration of polyepitope sequence in light of MHC motifs to exhaustively identify all junctional-free polyepitope designs for any given set of authentic epitopes, and in so doing discovered that the number of such variants of any given polyepitope can be astronomically high. Our approach designs polyepitopes of any length, considers multiple MHC class I or class II motifs simultaneously and can be adapted to design variants of existing proteins with pre-selected epitope contents. We have also implemented the algorithm as a computer-based tool (CANVAC II), which we make available to interested parties. The vast diversity of junctional-free polyepitopes suggests that the number of potential T-helper epitope free protein variants may also be large, which may have implications for discovery of bioactive but non-immunogenic therapeutics.