Understanding solution multiplicity of smoke flow at the same building configuration and ambient conditions is important for managing smoke flows and human evacuation in buildings. One of the known examples with solution multiplicity is in a simple single-compartment building on fire under an opposing wind. The occurrence of multiple solutions of smoke flow is induced by competing wind and thermal buoyancy forces. Under a given and moderate wind, the critical buoyancy flux ratio for the existence of smoke flow multiplicity, which is a ratio between defined parameters representing buoyancy force and wind pressure, is related to building height and opening area, as shown using a zone model. Computational fluid dynamics (CFD) simulations were used here to evaluate whether the behaviour of smoke flow multiplicity was affected by the geometry and location of the fire source(s). Our simulation results were in good agreement with previous macroscopic analysis results. A floor fire source can produce the largest smoke flow rate in the buoyancy-dominated flow regime among the tested cases while two corner sources can produce the smallest smoke flow rate. A floor source had a relatively large smoke flow rate in the wind-dominated flow regime while a point source had relatively small smoke flow rate. Moreover, a larger critical buoyancy flux ratio and a larger range of fire power in which smoke flow multiplicity existed were found for a floor fire source than for other sources. Switching of smoke flow solutions in building fires was found to depend on the initial conditions and the magnitude of flow perturbations.