We consider properties of a steady two-dimensional isothermal low Mach-number counter-flow, into which a dilute loading of small spherical particles is introduced at the local gas velocity, at a finite axial distance from the stagnation plane for the axial velocity component of the gas. The particles are introduced on one side of that stagnation plane only, and the consequences of any subsequent velocity slip of the particles with respect to the local gas are examined. The self-similarity (planar symmetry in the axial coordinate, for most of the key dependent variables), familiar from particle-free counter-flow, also holds for the two-phase flow under these conditions. Results, obtained by Lagrangian tracking of the motion of a single particle, distinguish: the nonoscillatory trajectory of that particle for relatively small strain-rate, large drag-rate conditions (the particle does not cross the stagnation plane for the axial velocity component); and the oscillatory trajectory of that particle under relatively large strain-rate, small drag-rate conditions (the particle may cross the stagnation plane repeatedly). However, for the multi-particle scenario for self-similar two-phase flow, the results for both conditions have commonalities. A single, densely particle-loaded, very thin slab region arises: one planar side of the slab interfaces with a particle-free, purely gaseous counter-flow, and constitutes the axial stagnation plane for that flow; the other planar side of the slab interfaces with a dilutely particle-laden region, in which the particle behavior is unaltered by the presence of the close-packed thin slab. In fact, the thin slab effectively is the stagnation plane for the axial velocity component of the gas, the value of the strain-rate/drag-rate ratio characterizing whether the plane is displaced from its pure gas counter-flow position (and, if so, to what different axial position).