Density-functional theory is used to study the geometric and electronic structure of cationic Si16+ clusters with a Ti, V, or Cr dopant atom. Through unbiased global geometry optimization based on the basin-hopping approach, we confirm that a Frank-Kasper polyhedron, with the metal atom at the center, represents the ground-state isomer for all three systems. The endohedral cage geometry is thus stabilized even though only VSi16+ achieves electronic shell closure within the prevalent spherical potential model. Our analysis of the electronic structure traces this diminished role of shell closure for the stabilization back to the adaptive capability of the metal-Si bonding, which is more the result of a complex hybridization than the originally proposed mere formal charge transfer. The resulting flexibility of the metal-Si bond can also help to stabilize non-magic cage-dopant combinations, which suggests that a wider range of materials may eventually be cast into this useful geometry for cluster-assembled materials.