This paper deals with the combination of the evolver dynamics of a hydrogen-like quantum system with the conical PREVTH (Probabilistic Evolution Theory) and excessively with the single monomial PREVTH. The new original applications are degree escalations in each monomial of a set of Poisson Bracket equations with multinomial right hand side and arbitrary, optimisable, parameters insertion to the resulting single monomial via an approach based on commutativity relations amongst the system basis operators. What we have shown that the additions based on commutativities with the Constancy Adding Space Extension (CASE) operator which is in fact proportional to identity operator, does not contribute to the suppression of the norm square of the single monomial coefficient matrix. This is just an observation for a specific family of systems but may be signaling a more general reality. If so it needs rather a rigorous proof.