You asking about reducing the dimension of already dimensionally reduced coarse grained system? I think we will lose lot of information then. But I don't know if there will be any symmetry existing in the system. It might depend on specific systems I guess. Maybe we can discuss on it if I am understanding your query in a wrong way.
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If there is a symmetry or some conserved quantity then you can reduce the system without losing any of the dynamics. I am not sure if that is the case for your set of equations. We can discuss it at a later time :o)