A pursuit-evasion problem for an interceptor (pursuer) and a maneuverable target (evader) is considered. It is assumed that during the engagement the system overcomes multiple abrupt changes. This leads to a formulation of a pursuit-evasion game for a switched piecewise-linear system. In the case of complete information on the switch timing and on the system matrices, the differential game is solved based on the zero-effort miss distance in the switched system. In the case where switch moments and system matrices are unknown to one of the players, two matrix games (pursuit game and evasion game) are formulated.