This paper presents an extension of a recently proposed hierarchical control framework applied to a cryogenic system. While in the previous work, each sub-system in the decomposition needed to show at least one component of the control input, in the present contribution, this condition is removed enabling a higher flexibility in the definition of the decomposition graph. The impact of this extended flexibility on the computation time is shown using the same cryogenic station where a decomposition in four sub-system is made possible (instead of two in the previous setting).