I am sure there is an answer to your question, but I'm not sure what it is. Let's see, If you lengthen the scale, then you need fewer strings. But, just how long you make the neck would be limited by how long your arms are. Now, by adding strings, you can keep the neck short, but you have to make it wider. Then the question that must be answered first is, "How large are your hands?" and opposed to, "How long are your arms?" So, we could assert that one string is sufficient provided one has very long arms (at least a very long left arm), or conversely, that one could use as many strings as the size of one's left hand will allow.
I know your question is a rhetorical one. I just feel the need to wax on when I see these bizarre looking instruments. Perhaps I'm simple, but I really appreciate the fact that I have four fretting fingers and my ukulele has four strings. I can live happily with the limited range. It's enough for me to try to master.