Plimmerian,
To give an example of how it could help find your Unknown, though my example is at a slightly closer level than 4th cousin.
I have a predicted 3rd cousin who has no Ancestry tree. He knows the name of his grandmother, Smith (literally, not an example!), and thinks she was born in either Scotland or Liverpool. Nothing else. 1939 Register and death record give different years of birth, 1906 or 1909.
He is a shared match with my paternal cousin and a couple of other matches who I know to be connected to my Laversuch family, so a working assumption could be that he is connected through this family.
I know that one Laversuch sibling 'married' or cohabited with a Smith, and had several children, including 8 boys and 3 girls. I am unable to trace all of these children after 1901 census, but a daughter of one of them would make the estimate of 3rd cousins correct.
I have provisionslly added an extra 'Unknown' child of Smith and Laversuch to my tree, adding
'Parentage
Not A Smith, not B Smith, unlikely to be C Smith, not D Smith -- Possibly E Smith, F Smith, G Smith or H Smith, or one of the girls'.
And that's as far as I can get, without finding the birth record of grandmother of my match.
New records may become available, closer matches may turn up, but the likelihood of me finding out his 'Unknown' is pretty slim. And he isn't particularly interested.
It is different in your case, you have no idea as to which surname could possibly connect you to your matches, so it will make it that much harder. As I said in my first post, patience, hard work and a great deal of effort.
Regards Margaret
Modified.
You, looking for Unknown, would only have Smith to go work on. You wouldn't know about Laversuch, there isn't a Smith/Laversuch marriage to help you, there would just be the three shared matches, who you may or may not be able to tie together, as there isn't much to go on in 3 of the trees.
You are in fact looking for someone a generation further back, and it becomes more difficult, but not impossible.
