Motivated in part by the success of WiFi, there has been much interest in opening up new 'prime' bands of spectrum for unlicensed use. Such bands can lower the cost for new wireless service providers to enter a market. The increased competition could in turn improve economic welfare. However, the openness of such spectrum can also lead to it becoming over congested, which in turn could deter investment. Indeed, a recent paper shows that due to the risk of congestion, only a single service provider may invest in a given unlicensed band and charge monopoly prices. However, that paper considers only a single band of unlicensed spectrum. In this paper, we consider investment and competition when there are multiple unlicensed bands available. In such a setting, each service provider could either invest in a single band or spread its investment over multiple bands. We consider a two-stage game for such a setting, in which firms first decide investment levels and second compete for customers by announcing prices for their service. The equilibria and resulting welfare of this game are characterized.