Modeling multivariate data that are subject to missingness requires making assumptions about how the missing data arise. We introduce the concept of the missing data being itemwise missing at random (IMAR) when each random variable is conditionally independent of its missingness indicator given the remaining variables and their missingness indicators. We show that this assumption leads to a non-parametric saturated class of models and illustrate how to use it with a number of examples. We also show how to perform sensitivity analysis and explore how the IMAR assumption can be relaxed using marginal information from auxiliary sources.