Multilist capture-recapture methods are commonly used to estimate the size of elusive populations. In many situations, lists are stratified by distinguishing features, such as age or sex. Stratification has often been used to reduce biases caused by heterogeneity in the probability of list membership among members of the population; however, it is increasingly common to find lists that are structurally not active in all strata. We develop a general method to deal with cases when not all lists are active in all strata using an expectation maximization (EM) algorithm. We use a flexible log-linear modeling framework that allows for list dependencies and differential probabilities of ascertainment in each list. Finally, we apply our method of estimating population size to two examples.