We study maximum likelihood estimation of the finite population mean for a survey experiencing unit nonresponse, when post-stratification information is externally available, possibly from multiple sources. Without external information, unit nonresponse may lead to data which is missing not at random. Analyzing such data would often require a model for the missing-data mechanism. However, modeling the mechanism can be challenging, and parameters are often poorly identified. Little et al (2017) introduced partially ignorable missingness for a subvector of the parameters. We extend their partially ignorable definition to situations where missingness can be assumed to depend additively on post-stratifiers. We develop a unified framework based on constrained optimization for diverse data types. We empirically study, as a special case, estimation of the finite population mean of a binary survey variable, when a categorical covariate is observed for the entire sample and a categorical post-stratifier is available for the entire population. For this example, we compare and contrast the proposed method to existing design-based estimators via simulations.