We show that the interplay between spin-changing collisions and quadratic Zeeman coupling provides a novel mechanism for the formation of repulsively bound composites in high-spin fermions, which we illustrate by considering spin flips in an initially polarized hard-core 1D Mott insulator of spin-3/2 fermions. We show that after the flips the dynamics is characterized by the creation of two types of exciton-biexciton composites. We analyze the conditions for the existence of these bound states, and discuss their intriguing properties. In particular we show that the effective mass and stability of the composites depends non-trivially on spin-changing collisions, on the quadratic Zeeman effect and on the initial exciton localization. Finally, we show that the composites may remain stable against inelastic collisions, opening the possibility of novel quantum composite phases.