Why does the stretching of spacetime have no limit? If multiple universes exist. Wouldn't each universe occupy a defined area? If these universes do occupy a defined area wouldn't there be a limit to another universes' intrusion on that space therefore limiting the amount of stretching?
Spacetime can be stretched as much as you want. Indeed, at the singularity in a black hole the stretching becomes infinite, though I'd guess most of us think some quantum effects become important near the singularity and prevent it actually becoming infinite.
Note that the volume within some region is coordinate dependant i.e. the value of the volume will depend on the observer doing the measuring. A good example of this is the volume inside a black hole event horizon. This is discussed in the question Do black holes have infinite areas and volumes?, though note that the answers are somewhat technical. Anyhow, the volume as measured by an observer inside the universe can be greater, possibly much greater, than the volume measured by an observer outside the universe.
Exactly what goes on in a multiverse depends on what assumptions you make about the structure of the multiverse. Typically the multiverse ideas stem from eternal inflation so the spacetime outside the universes is inflating faster than the universes can expand. So there is plenty of room for them all. Despite this it is possible for universes to collide and overlap, and there have been various (inconclusive) efforts to look for signs of this in the cosmic microwave background.
The stretching is just for visualization.
However, the most important contribution of Minkowski's geometric viewpoint of spacetime turned out to be in Einstein's later development of general relativity, since the correct description of the effect of gravitation on space and time was found to be most easily visualized as a "warp" or stretching in the geometrical fabric of space and time, in a smooth and continuous way that changed smoothly from point-to-point along the spacetime fabric.
There are too many undefined speculations in your question, to give a meaningful answer. What do you mean by 'the limit of stretching'? What do you mean by 'a universe occupying an area'?
There are many different theories for multiple universes or a mutiverse: http://en.wikipedia.org/wiki/Multiverse