Abstract. One-dimensional stationary flows of a plasma consisting of two ion populations and electrons streaming against a heavy ion cloud are studied. The flow structure is critically governed by the position of sonic and critical points, at which the flow is shocked or choked. The concept of sonic and critical points is suitably generalized to the case of multi-ion plasmas to include a differential ion streaming. For magnetic field free flows, the sonic and critical loci in the (u_px, u_hx) space coincide. Amongst the different flow patterns for the protons and heavy ions, there is a possible configuration composed of a "heavy ion shock" accompanied by a proton rarefaction. The magnetic field introduces a "stiffness" for the differential ion streaming transverse to the magnetic field. In general, both ion fluids respond similarly in the presence of "ion obstacle"; the superfast (subfast) flows are decelerated (accelerated). The collective flow is choked when the dynamic trajectory (u_px, u_hx) crosses the critical loci. In specific regimes the flow contains a sequence of solitary structures and as a result, the flow is strongly bunched. In each such substructure the protons are almost completely replaced by the heavies. A differential ion streaming is more accessible in the collective flows oblique to the magnetic field. Such a flexibility of the ion motion is determined by the properties of energy integrals and the Bernoulli energy functions of each ion species. The structure of flows, oblique to the magnetic field, depends critically on the velocity regime and demonstrates a rich variety of solitary and oscillatory nonlinear wave structures. The results of the paper are relevant to the plasma and field environments at comets and planets through the interaction with the solar wind.