It has become clear that there are multiple “moralities”: diverse bases that guide people’s judgments of right and wrong. The widely known Moral Foundations Theory (MFT) stipulates that there are at least five such moralities, measurable via questionnaire, and tends to assume that these distinct foundations are rooted deep in humanity’s evolutionary past. Were this true, we should find that the structure of five foundations is cross-culturally generalizable. Such assumptions are best tested in a diverse range of global populations with no built-in Western bias. We tested the measurement invariance of the short-form Moral Foundations Questionnaire (MFQ) across 27 countries spanning the five largest continents. We found it difficult to specify MFQ items in a quantitative five-factor model that would converge non-problematically across a wide variety of populations. We had some success specifying an alternative five-factor model based on the same items; however, for the most part this alternative model tapped constructs differing from what MFT intends, and it still remained far from good fit and any type of invariance. Thus, a stringent cross-cultural test reveals the lack of coherent structure in the inventory. Signs of ethnocentric bias in the construct formulations were also detected. Identified are better routes to identifying a set of multiple moralities-dimensions with potential for cross-cultural replication, and to building an inventory that would better approach factorial invariance across cultures.