Specify which template/layout to use based on URI segment I have 3 level structure for my entries with separate template for each level.

/artists/artist-name/ uses artists/_types/artists.html template

/artists/artist-name/section-name/ uses artists/_types/section.html template

/artists/artist-name/section-name/project-name/ uses artists/_types/project.html template

What I need to do is to specify additional layout for level 3 entry so depending on URI I can display one or another.

This is the additional URI I want to use:
/artists/artist-name/section-name/project-name/thumb and I want to load the artists/_types/thumb.html template
I'm not completely sure about what you're asking, but you might want to look in to craft.request:
 https://craftcms.com/docs/templating/craft.request

In your structure template, you can check your URL segments, and use twig include to load the desired template, based on those segments. 

Another related feature is dynamic routing:
https://craftcms.com/docs/routing#dynamic-routes

You could use this to route a URL to a different template.