The problem of an expanding chain (it already has some facilities) in a given area is considered. It may locate a new facility, or vary (up or down) the quality of its existing facilities, or close some of them, or a combination of all those possibilities, whatever it is the best to maximize its profit, given a budget for the expansion. A new competitive location (and design) model is proposed which allows all those possibilities. The resulting model is a difficult to solve MINLP problem. A branch-and-bound method based on interval analysis tools is proposed to cope with it, which can solve medium-size problems in a reasonable amount of CPU time. An ad-hoc heuristic and a hybrid method are also proposed, which usually find a (near)-optimal solution in a fraction of time of the exact method. Some computational studies are presented to show the performance of the algorithms.