Most ecosystems have multiple-plant invaders rather than single-plant invaders, yet ecological studies and management actions focus largely on single invader species. There is a need for general principles regarding invader interactions across varying environmental conditions, so that secondary invasions can be anticipated and managers can allocate resources toward pretreatment or postremoval actions. By reviewing removal experiments conducted in three Hawaiian ecosystems (a dry tropical forest, a seasonally dry mesic forest, and a lowland wet forest), we evaluate the roles environmental harshness, priority effects, productivity potential, and species interactions have in influencing secondary invasions, defined here as invasions that are influenced either positively (facilitation) or negatively (inhibition/priority effects) by existing invaders. We generate a conceptual model with a surprise index to describe whether long-term plant invader composition and dominance is predictable or stochastic after a system perturbation such as a removal experiment. Under extremely low resource availability, the surprise index is low, whereas under intermediate-level resource environments, invader dominance is more stochastic and the surprise index is high. At high resource levels, the surprise index is intermediate: Invaders are likely abundant in the environment but their response to a perturbation is more predictable than at intermediate resource levels. We suggest further testing across environmental gradients to determine key variables that dictate the predictability of postremoval invader composition.