Quench propagation velocity in conductors having a large amount of stabilizer outside the multifilamentary area is considered. It is shown that the current redistribution process between the multifilamentary area and the stabilizer can strongly effect the quench propagation. A criterion is derived determining the conditions under which the current redistribution process becomes significant, and a model of effective stabilizer area is suggested to describe its influence on the quench propagation velocity. As an illustration, the model is applied to calculate the adiabatic quench propagation velocity for a conductor having a multiply connected stabilizer, consisting of an inner core and an outer sheath.