The streaming instability is a fundamental process that can drive dust–gas dynamics and ultimately planetesimal formation inprotoplanetary discs. As a linear instability, it has been shown that its growth with a distribution of dust sizes can be classifiedinto two distinct regimes, fast- and slow-growth, depending on the dust-size distribution and the total dust-to-gas density ratio . Using numerical simulations of an unstratified disc, we bring three cases in different regimes into non-linear saturation. Wefind that the saturation states of the two fast-growth cases are similar to its single-species counterparts. The one with maximumdimensionless stopping timeτs,max=0.1 and =2 drives turbulent vertical dust–gas vortices, while the other withτs,max=2and =0.2 leads to radial traffic jams and filamentary structures of dust particles. The dust density distribution for the former isflat in low densities, while the one for the latter has a low-end cut-off. By contrast, the one slow-growth case results in a virtuallyquiescent state. Moreover, we find that in the fast-growth regime, significant dust segregation by size occurs, with large particlesmoving towards dense regions while small particles remain in the diffuse regions, and the mean radial drift of each dust speciesis appreciably altered from the (initial) drag-force equilibrium. The former effect may skew the spectral index derived frommultiwavelength observations and change the initial size distribution of a pebble cloud for planetesimal formation. The latteralong with turbulent diffusion may influence the radial transport and mixing of solid materials in young protoplanetary discs.