Extend template conditionally in Twig

Take the following tree structure:

├───base
│   ├───0001
│   │   └───pages
│   │           file.twig
│   │           file_content.twig
│   └───ext
│       └───store
│       │   └───pages
│       │       └───all
│       │       │       file.twig
│       │       └───0001
│       │               file.twig
│       └───newsletter
│           └───pages
│               └───all
│               │       file.twig
│               └───0001
│                       file.twig
└───pages
    │   file.twig
    └───0001
            file.twig

As you can see, there's a load of file.twig scattered around.

I want to render the contents of the file base/0001/pages/file_content.twig.
But, I want that the following files can change the content inside blocks:

• ext/<...>/pages/0001/file.twig
• ext/<...>/pages/all/file.twig
• /pages/0001/file.twig
• /pages/file.twig

But, these files may or may not exist, may or may not be needed and must be able to change the content of any block.

Is there any way to make this work?

So far, I have the following:

{% embed 'base/pages/file_content.twig' %}
    {% block page_file %}
        {{ parent() }}
        {% if data.store_enabled %}
            {% include [
                    'base/ext/store/pages/0001/file.twig',
                    'base/ext/store/pages/all/file.twig'
                ] ignore missing
            %}
        {% endif %}
        {% include ['pages/0001/file.twig', 'pages/file.twig'] ignore missing %}
    {% endblock %}
{% endembed %}

This "works", in the sense that it renders the page but doesn't allow any block to be overrided.

How could I make this work?

As an example, consider this structure of files (yes, files are missing, and that's expected):

    ├───base
    │   ├───0001
    │   │   └───pages
    │   │           file.twig
    │   │           file_content.twig
    │   └───ext
    │       └───store
    │       │   └───pages
    │       │       └───0001
    │       │               file.twig
    └───pages
            file.twig

The file base/0001/pages/file_content.twig has the following:

{% block page_file %}
    {% block title %}<h1>Nice title</h1>{% endblock %}
    {% block price %}{% endblock %}
    <div class="clearfix"></div>
{% endblock %}

The file base/ext/store/pages/0001/file.twig has the following content:

{% block price %}<span class="price">55 &euro;</span>{% endblock %}

And the file pages/file.twig has:

{% block title %}{{ parent() }}<hr>{% endblock %}
{% block price %}<div>{{ parent() }}</div>{% endblock %}

The output I expect is the following:

<h1>Nice title</h1><hr>
<div><span class="price">55 &euro;</span</div>
<div class="clearfix"></div>

But with that code, all the other files' changes are being ignored and the output is being only the following:

<h1>Nice title</h1>
<div class="clearfix"></div>

Note:

It's important to notice that I'm using Twig 1.33.2, and using the Twig_Autoloader::register(); method.

I can't use Twig 2.x, since it requires PHP 7.0+ and I'm restricted to PHP 5.3.29.