note that in this case at least few mutations are required only to improve an existing function (improving binding actually). thus, we can conclude that we need more than just few mutations to get a completely new function. (i came across an article recently, that also probably talks about a number of specific mutations but I do not find it at the moment).
according to the author: “If our results are general - and we think they probably are - then many of our body’s systems work as they do because of very unlikely chance events that happened in our deep evolutionary past,”.
from the article: " In screening thousands of alternative histories, the researchers found no alternative permissive mutations that could have allowed the protein’s modern-day form to evolve". “Among the huge numbers of alternate possible histories, there were no other permissive mutations that could have opened an evolutionary path to the modern-day GR,” Thornton said"
so what makes you think otherwise?