A linear-response formulation of the dc spin pumping, i.e., a spin injection from a precessing ferromagnet into an adjacent spin sink, is developed in view of describingmany-body effects caused by spin fluctuations in the spin sink. It is shown that when an itinerant ferromagnet near T-C is used as the spin sink, the spin pumping is largely increased owing to the fluctuation enhancement of the spin conductance across the precessing ferromagnet/spin sink interface. As an example, the enhanced spin pumping from yttrium iron garnet into nickel palladium alloy (T-C similar or equal to 20 K) is analyzed by means of a self-consistent renormalization scheme, and it is predicted that the enhancement can be as large as tenfold.