Yes- 1 gene there are 4 possibilities. 2 genes there are 16 possibilities. 3 genes 64 possibilities. It grows at an exponential rate. What I don't know, and can't seem to find anything definitive on, is just exactly how many genes are involved in making brown eggs. Everyone says it's "a lot" but there has to be a fact somewhere that that opinion is based on. I just can't seem to find it. Until I see something definitive I'm going to assume two factors.
I believe that no one knows how many genes are potentially involved, and some inhibit rather than produce brown, so if a hen lays a white egg, it could be missing the brown genes, or have the inhibitor genes.
And if you finally decide there are X, what if someone discovers a new one ? I don't know the number, but 2 seems far too easy to map and explain, so that is very unlikely to be the number. I would suggest at least 4, probably 10 or more.