Cube Limit

Given the relationship of cost centers to entities you describe, where any given cost center belongs to only one entity, I see cost centers naturally rolling up to entities and would keeps them all in the same dimension type.  

With each cost center relating to only its entity, there most likely isn’t a reporting or data entry use case that would benefit from intersecting these using different dimension types.  

I would roll them up to their entity based on the info here.  I don’t think you give up much flexibility with single member sparsity by keeping things fairly simple.