Firstly, let me confirm that my definition for right shift is correct: a right shift entails an increased ratio of product to reactant.
Say you have the reaction A -> B. The standard notion is that increasing concentration of the reactant shifts the equation to the right but that can obviously not be the case here. Explanation: Take two systems composed of A -> B respectively and add them together. You'll end up with 2A -> 2B with the ratio remaining the same.
However, if you have the equation A + B -> C, what will happen is that a greater percentage of B will react, and then the equation will shift to the right relative to B, but to the left relative to A, and to the left relative to the equation as a whole. However, if you increase both A and B by the same factor no shift will occur.
My overarching question is then whether I'm correct stating the above, and whether as I've described shifts left and right occur not relative to a side of the equation but rather relative to a specific part of it.