Templates for Custom Post Types

Because it’s a lot easier for my clients, I tend to use Custom Post Types (CPTs) for pretty much everything. In a current project, the client would like to have different blocks (e.g. CTA for newsletters, contact, trainings, etc.) to be linked in the sidebars of various pages and posts, so I created a simple CPT for the info blocks.

Now, some of these blocks should have some dynamic functionality (e.g. get some testimonials out of some database, etc.), so I wanted to create a custom template for these cases.

Is it possible to register different templates for CPTs, so that the client may choose these in the backend of the specific CPT? I’m looking for a functionality similar to the templates of pages.