This investigation is situated within an ongoing project which seeks to understand student thinking in upper-division introductory quantum mechanics courses. Recently, the Quantum Mechanics Concept Assessment (QMCA) was revised to include additional items in spin-basis contexts to reflect the rising prevalence of the "spins-first" instructional paradigm. In this work, we utilize exploratory factor analysis to group items on the QMCA based on common variance. Student responses were collected from several large institutions over the 2018-2019 academic year, with the three largest institutions following a "spins-first" curriculum. In interpreting our factor structure, we focus on the placement of isomorphic questions and the original concept framework of the QMCA, as well as a tentative interpretation of factor groupings. We conclude by discussing how these groupings may be further investigated, as well as implications for subsequent iterations of the QMCA and research on student thinking in these two contexts.