Nudge in the right direction for sub theme

I think I get the idea of theme inheritance, but I’m a little lost as to where to start. Basically I have a modular, one page site that uses theme A, and I want to have 1 page that uses theme B. I need to have a different page structure too, so I have to change the base.html.twig.

How do I get this one page to use the new template? Do I just create an alternate base template and then just extend the template file to use the new base file like this?
{% extends 'partials/base.html.twig' %}

Sounds very good. But then you need a second modular-b template as well that extends the base-b-template. (Maybe you can define the base layout via header).