WordPress - enable adding child pages with CPT slug as parent

I'm developing a WP site with multiple CPTs (all created with CPT UI plugin). Additionally I've created pages that have the CPT slug as its permalink (eg. [login to view URL]). Now I want to add child pages where the specific CPT page will be its parent (eg. [login to view URL]). Now when I create such page it throws a 404 error when opening it. I use pretty permalinks. In another words I need to be able to achive ALL the following: 1. All my CPT posts need to be visible normally under [login to view URL]; 2. I need to have pages with the same slug as the CPT ([login to view URL]); [the above two is no problem so far] 3. I need child pages like [login to view URL] (and here is the problem). Please don't send me generic offers without reading of rethinking your proposal. Just to make sure you've at least read the description, please include in the top of your reply the phrase "CPT child page".