Admission interviews in higher education may be developed with the intention to select applicants with specific personal competences not captured by traditional grade-based admission. In this study, we examined whether the data structure of multiple-mini admission interview scores supported the presence of communication, empathy, collaboration, and resilience as independent test dimensions. In addition, the associations between the interview scores and unintended test constructs (station format, pre-university grades, age, gender) were examined. Confirmatory and exploratory factor analyses and regression analyses were used to examine interview data from a cohort of Danish medical school applicants. The proposed multi-dimensionality was not supported by the data structure. The influence of the unintended constructs examined was limited or non-existing. These results are in line with the scarce existing literature. This situation makes a priori claims that the multiple-mini interview can measure multi-dimensional personal competences inadvisable, and care should be taken about what is communicated to stakeholders.