The Flow Refueling Location Model (FRLM) is a flow-intercepting model that locates p stations on a network to maximize the refueling of origin–destination flows. Because of the limited driving range of vehicles, network vertices do not constitute a finite dominating set. This paper extends the FRLM by adding candidate sites along arcs using three methods. The first identifies arc segments where a single facility could refuel a path that would otherwise require two facilities at vertices to refuel it. The other methods use the Added-Node Dispersion Problem (ANDP) to disperse candidate sites along arcs by minimax and maximin methods. While none of the methods generate a finite dominating set, results show that adding ANDP sites produces better solutions than mid-path segments or vertices only.