I'd like to address this comment from the question:
I do not think the discussion about our research about our common
ancestors is of interest to anyone else, nor is it suited for the Q/A
design of this site.
Whether your research is of interest to anyone else is a different issue from wanting to conduct your collaboration in private. Your research can be of interest if you choose to make it so. If that were not the case -- if genealogists everywhere thought that there was inherently no interest in reading something else unless the family was your family -- there would be no point in anyone writing a blog about their research, writing articles for their local genealogy society newsletters, and so on, because no one would read the blog or newsletter.
One of the things I find valuable about the Q/A design of the site is that it allows us to share our problem-solving skills with others by using our own research as the basis for our worked examples. If I've done my job properly, then it shouldn't matter whose family is used as the example for questions like Using a card index to find Probate records? -- any person who is looking for family members in the same record set should be able to use the techniques I used to find the index entry for their own people and then find the records (assuming they haven't been lost).
By contrast, if you use Google to look for other instances of people studying the same family, you can find plenty of forums where people meet up because they have a common ancestor and then take the discussion off-line. Once the participants change email addresses or are deceased, these low-content threads are of very little use to anyone else. You might learn that someone saw some bit of information somewhere, but that's about it.
I think the genealogy industry does us all a great disservice by encouraging us to look at our own families and nothing else. It can be of great value to read blog posts, journal articles, and other works by genealogists who are working in the same time period and geographical area that you are researching in. The reader can see what sources the author consulted and what information was discovered in the records, what other works were consulted to get background information on the problem, and so on. Examining case studies is of great value.
I don't mean to be critical of people who want to reach out to others working on the same lines, or who prefer to carry out their collaborative research in private once they have done so. I understand the desire to work things out in private, instead of displaying all your intermediate work for everyone to look at. But you shouldn't use "no one else will be interested in our discussion about our family" as an excuse for not sharing your work.