Depends on what you are calling "high white". Using it as a descriptor, yes there is a dominant "high white" and a recessive "high white". In the rat hobby "high white" is used to refer specifically to the dominant spotting that can result in megacolon. Unfortunately that is misleading (and the reason I hate the term) because the recessive hooded allele (as it is called in the scientific world and rat hobby) can also create a lot of white ("high white"). Personally I think the term should be thrown out completely and the animals should be described as what they are genetically... either they have the hooded allele, or they have dominant spotting. Dominant spotting is associated with megacolon, where the hooded allele is not.
Unfortunately these genes can also be combined, and that's where it gets tricky.