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I found it very difficult to understand your problem.
Based on what i understood
T1 < T2 = 1:M
T2 < T3 = 1:M
T3 < Fact = 1:M
T4< Fact = 1:M
simplest way to represent this as Star in BMM is
Create a Logical Table T3 with T3, T1 and T2 in the LTS
Create logicla table T4 and Fact
So you will have a perfect star in BMM T3< Fact> T4.
In physical layer it is still going to snowflake T1< T2< T3<Fact>T4 whatever you do.
So I think you are complicating things too much by adding T2 and T3 in Fact logical table.
Hope it helps.