With nonignorable missing data, likelihood-based inference should be based on the joint distribution of the study variables and their missingness indicators. These joint models cannot be estimated from the data alone, thus requiring the analyst to impose restrictions that make the models uniquely obtainable from the distribution of the observed data. We present an approach for constructing classes of identifiable nonignorable missing data models. The main idea is to use a sequence of carefully set up identifying assumptions, whereby we specify potentially different missingness mechanisms for different blocks of variables. We show that the procedure results in models with the desirable property of being non-parametric saturated.