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I think CombinatorialFreeModule and CombinatorialAlgebra are the places to start.

The most sophisticated graded Hopf algebras implemented in Sage are, I think, the Steenrod Algebras (Also see the online source code), so that implementation may give you some ideas too.

Good luck -- I am personally interested in computations with differential graded algebras so I would love to see how you implement your classes.