Hi @vodjakxa
Lets consider we have a Home page and a Contact page.
1. I believe what you can try to do is to create two editable templates first. Let's say template-home and template-contact.
2. Once the templates are in place and working, you can try to extend the ootb page.
3. Then create two structures that extend the custom page you just created. Let's call them page-home and page-contact
4. Then create two structures, one for each tab. Lets call them tab-common and tab-specific.
Your pages and structures will look something like:

Note: Please ignore their location. There are better practices about how to store them (organized in better folders, add versions, maybe in different project the ui.apps etc)
5. In each of the page structures include the tabs that you need:

6. Tabs structures can contain whatever elements you need. For this example I simply added two text fields :

7. Then final step is to go in the template definitions and refer the two new page structures you just created: page-home and page-contact

Please be aware that I have not tested this on my local. I just quickly sketched it on paper, just to underline the concept. I hope I haven't omitted anything.