The Sonnerup merging model for an incompressible plasma is extended to allow a flow component along the field lines in the inflow regions. Solutions are found to exist as long as the difference between the quantities B. V for the two inflow regions does not exceed a critical magnitude dependent on the inflow field magnitudes and plasma densities. All such solutions satisfy Vasyliunas' definition of merging, but some classes of solution have radically altered geometries, i.e. geometries in which the inflow regions are much smaller than the outflow regions. The necessary but not sufficient condition for these unusual geometries is that the field-aligned flow component in at least one inflow region be super Alfvénic. A solution for the case of a vacuum field in one inflow region is obtained in which any flow velocity is allowed in the non-vacuum inflow region, although super-Alfvénic flow can still result in an unusual geometry. For symmetric configurations, the usual geometry, that of Petschek and Sonnerup, is retained as long as both field-aligned flow components in the inflow regions are less than twice the inflow Alfvén speed. For the case of a vacuum field on one side and fields approximating the boundary between the solar wind and the earth's dayside magnetosphere, the usual geometry is retained for flow less than about 2·5 times the local Alfvén speed.