It seems to me that it should be possible to install WordPress in a folder on a WordPress website, but when I did this, I had a problem that I couldn't resolve.
I installed WordPress in a folder called "members" inside a WordPress website. The install was done using cpanel's site software installation routines, so if there were any error or warning messages generated, I didn't see them.
The problem I had with the site was the the landing page always gave me a page not found error.
When the posts list was the landing page I got a page not found error every time I went to the landing page http://domainname.com/members/
I changed the "Reading" parameter to make a page called "Welcome" the home page. When I did that, clicking on Welcome in the navigation menu resulted in a page not found. So I changed the landing page to "About". Then clicking on Welcome resolved correctly, but clicking on "About" resulted in a page not found.
This was the case when I used the default page naming, and when I changed permalinks to the name of the post.
Is it possible to get a working installation of WordPress going inside a folder of a WordPress website? What do I need to do to get around this landing page problem? Or did I mess up some aspect of the installation?