It is widely known that the fully deprotonated form of EDTA (usually written as Y4-) is the only form that is significantly involved in complexation reactions. From what I have read, this accounts for the fact that the fully deprotonated form has the highest number of complexation sites (the other protonated forms obstruct oxygen atoms from interacting with the metal since those atoms bear protons). Hence, this form has the largest constant of formation, Kf, given the thermodynamical implications of the chelation effect. Also, correct me if I am wrong, but this is exactly the reason why complexometric titrations that use EDTA as a titrant are carried out for a specific metal ion at a fixed pH - at that pH value, the fully deprotonated form has the maximum concentration it could have while also avoiding the precipitation of the metal ion as a hydroxide.
Out of sheer curiosity I looked for any experimental or theoretical evidence to find out whether or not the other protonated forms were involved as well in this complexation equilibria. Even though their influence is neglected (because their formation constants are orders of magnitude smaller than our main Kf), I am still interested to hear to what degree do they participate in complexation with the metal.
To my disappointment, I have found no explicit answer to my question. The two analytical chemistry textbooks I have been studying from (Gary D. Christian, Purnendu K. Dasgupta, Kevin A. Schug - Analytical Chemistry-John Wiley & Sons (2013) and Douglas A. Skoog, Donald M. West, F. James Holler, Stanley R. Crouch - Fundamentals of Analytical Chemistry-Cengage Learning (2013)) covered this topic briefly, but failed at offering any insightful information.
To sum up, are the other partially protonated forms of EDTA involved in complexation equlibria with metallic ions? If yes, to what extent, what are their formation constants? Also, feel free to correct every scientific detail that I have mentioned you might disagree with.