This paper provides a first investigation of twice-mobile networks, i.e., cellular networks where both the end users and (part of) the radio access network infrastructure are mobile. Twice-mobile networks are based on an opportunistic, dense, crowdsourced, random deployment of mobile small cell base stations carried by vehicles, and on millimetre-wave backhaul connections between the mobile small cell base stations and the fixed network elements. Thanks to the fact that vehicles carrying mobile small cell base stations roam coherently with mobile subscribers, twice-mobile networks provide adaptive broadband wireless capacity where and when users need it, thus avoiding the cost and intrinsic inefficiency of dense deployments of fixed small cell base stations. In this paper we investigate the achievable capacity under the twice-mobile network paradigm, using real-world telecom traffic and vehicle positions in two case studies in Milan, Italy. Our results show that, thanks to positive spatial correlations between mobile net- work demands and road traffic, mobile small cell base stations carried by vehicles ensure performance equivalent or better to that of a traditional deployment of fixed small cells, at significantly lower cost. pub