  We extend the preorder on k-tuples of dominant weights of a simple complex
Lie algebra g of classical type adding up to a fixed weight $\lambda$ defined
by V. Chari, D. Sagaki and the author. We show that the induced extended
partial order on the equivalence classes has a unique minimal and a unique
maximal element. For k=2 we compute its size and determine the cover relation.
  To each k-tuple we associate a tensor product of simple g-modules and we show
that for k=2 the dimension increases also along with the extended partial
order, generalizing a theorem proved in the aforementioned paper. We also show
that the tensor product associated to the maximal element has the biggest
dimension among all tuples for arbitrary k, indicating that this might be a
symplectic (resp. orthogonal) analogon of the row shuffle defined by Fomin et
al.
  The extension of the partial order reduces the number of elements in the
cover relation and may facilitate the proof of an analogon of Schur positivity
along the partial order for symplectic and orthogonal types.
