Item nonresponse in surveys is usually dealt with through single imputation. It is well known that treating the imputed values as if they were observed values may lead to serious underestimation of the variance of point estimators. In this article, we propose three pseudo-population bootstrap schemes for estimating the variance of imputed estimators obtained after applying a multiply robust imputation procedure. The proposed procedures can handle large sampling fractions and enjoy the multiple robustness property. Results from a simulation study suggest that the proposed methods perform well in terms of relative bias and coverage probability, for both population totals and quantiles.