It’s possible, but it will take a some coding and a little understanding of WordPress functions to get it done.
First, your members have to be WordPress users. You can set up a special user role for them or they can just be subscribers. I suggest using a plugin like “Front End Users” which gives them a profile page on the frontend. There are other membership plugins that do similar things.
Now, on a page that your users have to be logged in on, put your “signup” form. In this case, the purpose of the form is to let them add a title to their collection. You need to set up a hidden field that collects their username and stores it with the record. How to do that is explained in the “other notes” section here.
Now, it’s just a matter of setting up the user’s collection page so that it only shows the titles for a particular user and gives them a way to edit each one. This page also needs to be restricted to logged-in users only. Use a special WP template and include the list using the do_shortcode function, adding their username to the “filter” attribute so it only shows their titles. Add the “edit” link to the list using the instructions given in this blog post: adding an edit record link to the frontend list
These instructions are only a sketch, many details are missing.