We report on an experimental and theoretical systematic study of double ionization of helium by ion impact in terms of four-particle Dalitz plots. Several collision systems covering abroad range of perturbation parameters η (projectile charge to speed ratio) were investigated. With increasing η we observe a systematic trend from features, characteristic to correlated double-ionization mechanisms, to signatures of higher-order processes not requiring electron-electron correlations [the mechanism called "two-step-two projectile-electron interaction" (TS-2)]. The data for the largest η can qualitatively be amazingly well described by a simple model only including the TS-2 mechanism.