Quantum confinement in small symmetric clusters leads to the bunching of electronic states into closely packed shells, enabling the classification of clusters with well-defined valences as superatoms. Like atoms, superatomic clusters with filled shells exhibit enhanced electronic stability. Here, we show that octahedral transition-metal chalcogenide clusters can achieve filled shell electronic configurations when they have 100 valence electrons in 50 orbitals or 114 valence electrons in 57 orbitals. While these stable clusters are intrinsically diamagnetic, we use our understanding of their electronic structures to theoretically predict that a cluster with 107 valence electrons would uniquely combine high stability and high-spin magnetic moment, attained by filling a majority subshell of 57 electrons and a minority subshell of 50 electrons. We experimentally demonstrate this predicted stability, high-spin magnetic moment (S = 7/2), and fully delocalized electronic structure in a new cluster, [NEt4]5[Fe6S8(CN)6]. This work presents the first computational and experimental demonstration of the importance of dual subshell filling in transition-metal chalcogenide clusters.