We　study　the　submodular　maximization　problem　in　generalized　streaming　setting　using　a　two-stage　policy.　In　the　streaming　context,　elements　are　released　in　a　fashion　that　an　element　is　revealed　at　one　time.　Subject　to　a　limited　memory　capacity,　the　problem　aims　to　sieve　a　subset　of　elements　with　a　sublinear　size,　such　that　the　expecting　objective　value　of　all　utility　functions　over　the　summarized　subsets　has　a　performance　guarantee.　We　present　a　generalized　one　pass,　-approximation,　which　consumes　memory　and　runs　in　time,　where　k,　n,　m　and　denote　the　cardinality　constraint,　the　element　stream　size,　the　amount　of　the　learned　functions,　and　the　minimum　generic　submodular　ratio　of　the　learned　functions,　respectively.　©　2020,　Springer　Nature　Switzerland　AG.