I do not see a computational aspect of this question, so you may be better off asking elsewhere. That being said, I cannot see how using a mixture of antibodies would allow you to study the interaction of two proteins in transcription. If you have two antibodies that each target a different transcription factors, your ChIP would pull down DNA fragments bound by either of the two transcription factors. It would to my knowledge not give you any information on which transcription factor(s) bound which fragment.
If you want to understand to which extent the two transcription factors target the same set of downstream genes, I think they way to go is to do separate ChIP-seq experiments for the two transcription factors and then subsequently computationally analyze which promotors are bound by both transcription factors.
In principle you can. There is no specific reason why the mixture of antibodies would not work. And since you will eventually access the precipitated sequences themselves you might be able to make an educated guess which precipitated sequence comes from what transcription factor binding.
In ChIP-on-chip this is not unheard of. Since the chips are expensive to run you will want to maximize the amount of information you get from a single array. The trade off is likely different for ChIP-seq.
There may be specific reasons to combine antibodies though. Suppose it is really a complex you are looking at, and the binding of protein A is conditional for the binding of protein B, then you will only get signals for both TFs combined. This is something you might in fact want to study using 2 antibodies. Although you will still have to evaluate the binding sequences for each of them, you might even find that protein B doesn't have a binding sequence of it's own but only piggy backs on protein A.