Many surveys have seen steep declines in response rates, threatening the validity of secondary analyses based on those incomplete data. Yet, government agencies and survey organizations are under increasing budgetary pressures, making less resources available for extensive nonresponse follow-up activities. In this environment, government agencies and survey organizations need new options for how they handle missing data. We develop such options by focusing on how to leverage information from auxiliary data sources, such as administrative records and databases gathered by private-sector data aggregators, in nonresponse adjustments. A method is developed for specifying imputation models so that (i) the models reflect realistic assumptions about the missing data mechanisms, (ii) the models take full advantage of auxiliary marginal information, and (iii) all parameters in the models can be uniquely estimated. The methodology is illustrated on an application examining voter turnout among subgroups of the population in the Current Population Survey (CPS). We utilize population-based auxiliary data from government election statistics available in the United States Elections Project.