The　BP　problem　maximizes　the　sum　of　a　suBmodular　function　and　a　suPermodular　function(BP)　subject　to　some　constraints,　where　both　functions　are　nonnegative　and　monotonic.　This　problem　has　been　widely　studied　under　the　single-stage　setting.　In　this　paper,　we　consider　a　variant　of　the　BP　maximization　problem.　The　problem　is　a　two-stage　BP　maximization　problem　subject　to　a　p-matroid　constraint,　for　which　we　propose　an　approximation　algorithm　with　constant　approximation　ratio　parameterized　by　the　curvatures　of　the　two　functions　involved.