Moral foundations theory posits five moral foundations, however 5-factor models provide poor fit to the data. Here, in five studies, each with large samples (total N = 11,496), we construct and replicate a well-fitting model of the Moral Foundations Questionnaire (MFQ). In study 1 (N = 2,271) we tested previously theorised models, confirming none provide adequate fit. We then developed a well-fitting model of the MFQ. In this model, the fairness/reciprocity and harm/care foundations were preserved intact. The binding foundations, however, divided into five, rather than the original three foundations. Purity/sanctity split into independent foundations of purity and sanctity. Similarly, Ingroup/loyalty divided into independent factors of loyalty to clan and loyalty to country. Authority/respect was re-focussed on hierarchy, losing one item to the new sanctity foundation and another into loyalty to country. In addition to these 7 foundations, higher-level factors of binding and individualizing were supported, along with a general/acquiescence factor. Finally, a “moral tilt” factor corresponding to coordinated left-leaning vs. right-leaning moral patterns was supported. We validated the model in four additional studies, testing replication of the 7-foundation model in data including from US, Australia, and China (total N = 9,225). The model replicated with good fit found in all four samples. These findings demonstrate the first well-fitting replicable model of the MFQ. They also highlight the importance of modelling measurement structure, and reveal important additional foundations, and structure (binding, individualizing, tilt) above the foundations.