Why might an earth quake have more than one intensity value?

Yes. The Mercalli intensity scale measures the effect of the earthquake on people and structures, and the intensity value will differ depending on how far you are from the epicenter.

For instance, a 5.5 magnitude earthquake may be damaging (intensity VII) around the epicenter, but 300 miles away it may be barely felt (intensity II).

The mercalli scale measures the intensity of an earthquake, where the Richter scale measures the magnitude.

Also you have to consider where the earthquake occurred. you can have a 9.0 quake in the middle of the Australian outback but there is hardly anybody there so you would have a low mercalli scale reading. If you had that same quake in San Francisco then you are going to have a seriously high number on the mercalli scale