Statistical approaches to dialog state tracking synthesize information across multiple turns in the dialog, overcoming some speech recognition errors. When training a dialog state tracker, there is typically only a small corpus of well-matched dialog data available. However, often there is a large corpus of mismatched but related data – perhaps pertaining to different semantic concepts, or from a different dialog system. It would be desirable to use this related dialog data to supplement the small corpus of well-matched dialog data. This paper addresses this task as multi-domain learning, presenting 3 methods which synthesize data from different slots and different dialog systems. Since deploying a new dialog state tracker often changes the resulting dialogs in ways that are difficult to predict, we study how well each method generalizes to unseen distributions of dialog data. Our main result is the finding that a simple method for multi-domain learning substantially improves performance in highly mismatched conditions.