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A battery-swapping station (BSS) can serve as a flexible source in distribution systems, since electric vehicle (EV) batteries can be charged at different time periods prior to their swapping at a BSS. This paper presents an EV battery service transformation from charging to swapping batteries for EVs for the capacity enhancement of a distribution system. A novel mathematical model is proposed to optimally quantify and maximize the flexibility of BSS loads in providing demand response for the utility operator while considering technical operations in the distribution grid. Case studies and numerical findings that consider data from the National Household Travel Survey and a 32-bus distribution system are reported and discussed to demonstrate the effectiveness of the proposed model. Offering battery-swapping services helps reduce not only the peak load, but also the station operation cost.