In the present paper a pure exchange, general equilibrium model is considered and the equilibrium set is studied. It is shown for all total endowments and an open and dense set of preferences that if there are l >= 2 commodities and m >= 2 consumers then there exists a set of distributions of endowments with nonempty interior such that the associated economies have at least l - 1 + min{l,m} equilibria for l + min{l,m} even and at least l - 2 + min{l,m} equilibria for l + min{l,m} odd.