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We study the superradiance dynamics in a dense system of atoms each of which can be generally a spin-j particle, with j an arbitrary half-integer. We generalize Dicke's superradiance point of view to multiple-level systems and compare the results based on a novel approach we developed previously [Lin and Yelin, Adv. Atom. Mol. Opt. Phys. 61, in press (2012)]. Using this formalism we derive an effective two-body description that shows cooperative and collective effects for spin-j particles, taking into account the coherence of transitions between different atomic levels. We find that superradiance, which is well known as a many-body phenomenon, can also be modified by multiple-level effects. We also discuss the feasibility and propose that our approach can be applied to polar molecules, for their vibrational states have a multilevel structure which is partially harmonic.
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