This paper analyses the effect on agglomeration tendencies of allowing firms to become multi-region firms in a standard model of trade and location. More specifically, we introduce horizontal and vertical multi-region firms into the core-periphery (CP) model developed by Krugman (1991). The introduction of horizontal multi-region firms dampens the strong agglomeration effects found in the CP model by making the range of trade costs for which the core-periphery equilibrium occurs smaller. The introduction of vertical multi-region firms that can separate the location of headquarter activities from the location of production has two counteracting effects. First, headquarters have a strong tendency to agglomerate, and, in this sence, agglomeration tendencies are strengthened. Second, actual production tends to be more spread out, and, in this sense, they are weakened.