When a ligand and receptor interact with a given kd, one can easily determine % of ligand bound to the receptor when the kd, total concentration of ligand, and total concentration of receptor are known. When there is a mixture of multiple ligands and receptors where each ligand and each receptor can interact with eachother, this is not so simple. For example, lets say you have the following set of information:

k11 = [a1][b1]/[a1b1]

k12 = [a1][b2]/[a1b2]

k21 = [a2][b1]/[a2b1]

k22 = [a2][b2]/[a2b2]

along with the kd's (kij) and the total concentrations of a1, a2, b1, and b2. I have not managed to find any publications where this has been demonstrated but I would be surprised if it hasn't been figured out by someone.