This paper proposes a general algebraic formulation able lo unify all the previous developments in (he frame of subgrid-scale modeling using dynamic mixed models. This formulation can serve as a guide for the design of new multi-parameter SGS models. All usual cases of coupling between momentum and energy (or transport) equation are treated formally, and properties of the associated linear or non-linear system are discussed. It is shown thai all the existing models found in the literature can be grouped into a seven-parameter dynamic model, referred to as the Maximal Complexity Dynamic Model (MCDM) A priori lests on this MCDM are carried out for the subsonic plane channel flow problem, which aim at selecting the most important contributions in multi-parameter dynamic models.