Hierarchy in separate dimension tables

Hi

I have got following situation.

I have personDim and a person can have three type of designation at a time say Designition1,Designition2,Designition3.

group of persons form a Team (a team has persons of three types of designation)

say, TeamA has three members PersonWithDesignition1,PersonWithDesignition2,PersonWithDesignition3

and team belongs to a particular department say Dept1 and Dept1 can have multiple teams however a team can have only one department at a time.

So, Hierarchy becomes

Dept1
-------------------
TeamA TeamB ....
-----------------------
PersonWithDesignition1
PersonWithDesignition2
PersonWithDesignition3

hierarchy: Department -> Team -> Persons

In current DW design all this is created using a bridge table. basically a bridge table is used to demonstrate this hierarchy and join three different dimensions as
Person,Team,Department.

Fact table is at Team level.

Do you think this could have been handled better way instead of putting hierarchies in separate dimension table. Is there any better way to handle this.