Purely by rule, there are no multiclass which is completely impossible and outright denied. A paladin/monk/assassin is not denied by the rules and could in theory be allowed. However, the more exotic one tries to mix the classes, the greater chance is that they will only remain as "in theory".
Extensive is a very loose term... "no one, to date, has ever been close to even have a chance to qualify" is also falling under that extensive category... which could make it de facto impossible.
ps. This is no regard to the particular multiclass you wrote about. All multiclasses are handled on a case-on-case basis.
ps 2. This is only valid for multiclasses. If we take everything together... race + deity + classes + alignment, then one might stumble upon those "not allowed at all" situations.