First of all, I’m assuming this もっとも is 尤も. If you think otherwise please let me know! Assuming that is correct,
I’m also inclined to think it is the first definition here, that is to say, the one that means the same thing as でも, as I was told this でももっと is not unlike しかしながら ( which I had never heard of prior, but according to a Japanese person it exists).
So! If it does indeed mean “but” as でも does, then why put both? 「でも」か「もっとも」だけに比べて、含みはどう違いますか？