If a node can have two parents, than the structure is not a tree, is it?
The answer is no - you can't have two parents for one category, since category's parent is defined as a foreign-key on the parent column in a one-to-many relationship. There is no way to assign two parents unless you change the underlying structure:
belongs_to :parent, :class_name => name, :foreign_key => configuration[:foreign_key], :counter_cache => configuration[:counter_cache]