The multiverse proposal changes the fine-tuning question by increasing the number of opportunities for life-permitting conditions to occur.
If different universes or domains contain different constants, laws, or initial conditions, most might be lifeless while some permit complex structures and observers. Observers would necessarily find themselves in one of the compatible regions because they could not exist in the others.
This combines a varied multiverse with an observer-selection or anthropic effect.
Multiverse ideas do not arise solely as responses to Intelligent Design. Versions of them have emerged from developments in cosmology and fundamental physics.
If a well-supported physical mechanism generates a sufficiently large and varied collection of universes, anthropic selection could help explain why observers encounter life-permitting conditions.
The explanatory power of a multiverse depends upon the kind of multiverse that actually exists. It must generate an appropriate range of physical conditions, and some way is needed to reason about probabilities among the resulting universes.
These questions lead to difficult problems involving probability measures, typical observers, and what a particular multiverse model should predict. Other universes are also difficult to test directly.
Does fundamental physics actually produce a sufficiently varied multiverse? If it does, can the theory make testable predictions about the conditions observers should expect to measure?
Intelligent Design proponents may accept that a multiverse could alter probability arguments about fine-tuning while asking whether the universe-generating system itself requires explanation.
However, design should not be protected simply by moving the argument whenever physics provides a successful explanation. A multiverse supported by independent evidence would have to be taken seriously when assessing the case.