Electoral studies consistently show a substantive difference between selfreported turnout, on one side, and validated turnout and official results, on the other side. As any inaccurate data, misreported voter turnout in surveys may lead to erroneous substantive conclusions. Extant efforts to reduce this source of bias focus mainly on the reduction of misreporting in surveys by manipulating question wording. We propose a new approach to attenuate the impacts of misreported voter turnout in surveys based on multiple overimputation (MO), a method for handling of data with measurement error proposed by Blackwell, onaker and King. We propose multiple overimputation of the selfreported turnout (MOST) using information obtained from extant surveys of the same population. We test our method in a Monte Carlo (MC) study as well as by comparing it to the validated turnout present in the American National Election Studies (ANES). We take the turnout as a response variable, compare the results produced by the selfreported, validated, and multiply overimputed turnout, and test if our approach reduces the bias produced by misreporting in the selfreported vote. MC evidence suggests that MOST improves the estimates even under conditions of relatively high volatility of population models of turnout and overreporting. In the field test MOST reduces the coefficient bias and Type I error rate. We discuss how our approach can be improved with hierarchical Bayesian modeling and mixtures.