This paper introduces a multi-species version of a process called ASEP (q, j). In this process, up to 2j particles are allowed to occupy a lattice site, the particles drift to the right with asymmetry q 2j ∈ (0.1), and there are n − 1 species of particles in which heavier particles can force lighter particles to switch places. Assuming closed boundary conditions, we explicitly write the reversible measures and a self-duality function, generalizing previously known results for two-species ASEP and single-species ASEP(q, j).Additionally, it is shown that this multi-species ASEP(q, j) is dual to its space-reversed version, in which particles drift to the left. As j → ∞, this multi-species ASEP(q, j) converges to a multi-species q-TAZRP and the self-duality function has a non-trivial limit, showing that this multi-species q-TAZRP satisfies a space-reversed self-duality.The construction of the process and the proofs are accomplished utilizing spin j representations of Uq(gl n ), extending the approach used for single-species ASEP(q, j). arXiv:1605.00691v1 [math.PR] 2 May 2016 then the duality should reduce to the ASEP(q, j) duality of [8] corresponding to the ith projection. Or, in other words, each ith class particle in ξ counts 1, . . . , ith class particles in η according to the ASEP(q, j) duality. Indeed, this paper will prove that this is indeed true.Additionally, in the j → ∞ limit, the asymmetry parameter converges to 0 and an arbitrary number of particles are allowed at each site. Indeed, the ASEP(q, j) process converges to the q-TAZRP (Totally Asymmetric Zero Range Process) introduced in [26]. A similar statement holds here: namely, the multispecies ASEP(q, j) process in this paper converges to a multi-species q-TAZRP constructed in [31]. Additionally, by applying a charge-parity symmetry, the self-duality function converges to a duality function between this multi-species q-TAZRP and its space-reversed version, in which particles jump in the opposite direction.During the preparation of this paper, the author learned in a private communication that an upcoming paper by V. Belitsky and G. Schütz [5] analyzes the n-species ASEP with closed boundary conditions (corresponding to j = 1/2 in the notation here) with Uq(gl n+1 ) symmetry and explicitly derives all invariant measures and a class of self-duality functions. Additionally, an application to the dynamics of shocks is proved.The reminder of this paper is organized as follows. Section 2 defines the process and states the results for duality and reversible measures. Section 3 goes over the [8] framework and the necessary representation theory background. Section 4 constructs the process using this framework. Section 5 proves the theorems concerning duality and reversible measures.Acknowledgments.