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»ã±¨ÌáÒª£ºIn this talk we develop Rubio de Francia extrapolation with quantitative bounds to investigate quantitative weighted inequalities for operators beyond the (multilinear) Calder\'{o}n-Zygmund theory. We mainly establish a quantitative multilinear limited range extrapolation, which refines a result of Cruz-Uribe and Martell. We also present an extrapolation from multilinear operators to the corresponding commutators. Additionally, our result is quantitative and allows us to extend special quantitative estimates in the Banach space setting to the quasi-Banach space setting.