In this chapter we introduce the symmetric partial exclusion process, which generalizes the standard symmetric exclusion process, by allowing a maximal particle number per site that can vary from site to site. Because there is an extensive literature on the exclusion process, both in the area of probability theory as well as in the area of quantum spin chains, we give here a concise discussion focusing on duality and intertwining from the algebraic point of view. We construct the single edge generator from the \(\mathfrak {su}(2)\) algebra generators, in a discrete representation labeled by the maximal number of particles. We show that the single edge generator of this process is related to the coproduct of the Casimir in a manner which is completely analogous to the computation for the symmetric inclusion process, but now in the setting of the \(\mathfrak {su}(2)\) algebra. Next we show that symmetric partial exclusion process has an additive structure given by copies of symmetric exclusion processes on a layered graph, similarly to what we proved in the setting of the symmetric inclusion process. This leads to intertwining of symmetric partial exclusion processes with different maximal occupation numbers. Finally, we consider a scaling limit where the maximal number of particles diverges, and find the deterministic process associated to independent random walkers.