Model Sparsity - Combination of Dimensions

I have a question about reducing sparsity in a model by using numbered lists to combine a series of dimensions.

I am using ledger data that has information by supplier and by department over time. If I create a module that is dimensioned by these I end up with a huge amount of sparsity as most suppliers are just used by 1 department (although some could be used by more than one). I would like to be able to create a module that each department could look at only their suppliers, reducing sparsity and also improving user experiences, whilst being able to deal with some suppliers being used across different departments.

How can I use the existing ledger data to create a space efficient list which can show the supplier costs by department over time?

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