multiple hierachi is possible with same dimension

You need to describe what "multiple hierarchy" could possibly be. Normally, the term "hierarchy" is associated with such as simple graph as tree. How can it possibly multiple or non-multiple. Your further description looks quite vague. You should better first describe the structure you keep in mind as formal relationship (if graph terms, set-theory terms or relational algebra terms, whatever seems more convenient for you), and then you could illustrate it in application terms, if it seems appropriate. Probably you would need more words to express it, but those words should be strict enough.

Some terms you are using are from relational databases. And it's known that relational model can express any preliminary defined relationship. Do you need help with modeling it? A database schema or something? Just explain more. What is your structure more exactly, what did you try and where do you see a blocker?

—SA