In　the　paper,　we　study　the　adaptivity　of　maximizing　a　monotone　nonsubmodular　function　subject　to　a　cardinality　constraint.　Adaptive　approximation　algorithm　has　been　previously　developed　for　the　similar　constrained　maximization　problem　against　submodular　function,　attaining　an　approximation　ratio　of　and　rounds　of　adaptivity.　For　more　general　constraints,　Chandra　and　Kent　described　parallel　algorithms　for　approximately　maximizing　the　multilinear　relaxation　of　a　monotone　submodular　function　subject　to　either　cardinality　or　packing　constraints,　achieving　a　near-optimal-approximation　in　rounds.　We　propose　an　Expand-Parallel-Greedy　algorithm　for　the　multilinear　relaxation　of　a　monotone　and　normalized　set　function　subject　to　a　cardinality　constraint　based　on　rounding　the　multilinear　relaxation　of　the　function.　The　algorithm　achieves　a　ratio　of,　runs　in　adaptive　rounds　and　requires　queries,　where　is　the　Continuous　generic　submodularity　ratio.　©　2020,　Springer　Nature　Switzerland　AG.