We　consider　a　two-stage　submodular　maximization　under　pmatroid　(or　p-extendible)　constraints.　In　the　model,　we　are　given　a　collection　of　submodular　functions　and　some　p-matroid　(or　extendible)　system　constraints　for　each　of　these　functions,　one　need　to　choose　a　representative　set　with　a　cardinality　constraint　and　simultaneously　select　a　series　of　subsets　that　are　restricted　to　the　representative　set　for　all　functions,　the　aim　is　to　maximize　the　average　of　the　summarization　of　these　function　values.　We　extend　the　two-stage　submodular　maximization　under　single　matroid　to　handle　p-matroid　(or　p-extendible)　constraints,　and　derive　constant　approximation　ratio　algorithms　for　the　two　problems,　respectively.　In　the　end,　we　empirically　demonstrate　the　efficiency　of　our　method　on　some　datasets.