Associated Category List from Products in a Particular Category

Question

I am working on a site where product brands have been set up as categories. Each product has at least 2 categories, one for brand and others for product categories.

On the page for Brand-X, rather than list the products, I wish to show all the other categories that are associated with Brand-X's products.

What would be the most efficient way to obtain a category list from this structure?

For example:

Product A - Categories [Brand-X, Category-1, Category-2]
Product B - Categories [Brand-X, Category-4]
Product C - Categories [Brand-X, Category-2]
Product D - Categories [Brand-Y, Category-3]

on the Brand-X page, display links to Category-1, Category-2, Category-4

Answer 1

I have used a join within the collection. Note this was used inside block, but I have included for the sake of the example.

    $collection = $this->_catalogLayer->getCurrentCategory()->getCollection()                            
                        ->addIsActiveFilter()
                        //limit the categories to the current store
                        ->addPathsFilter(1 . '/' . $this->_storeManager->getStore()->getRootCategoryId())                                              ;

    $collection->getSelect()
            ->join(['category_products' => 'catalog_category_product'], 'category_products.category_id = e.entity_id', [])
            ->join(['sub_categories' => 'catalog_category_product'], 'category_products.product_id = sub_categories.product_id', [])
            ->group('e.entity_id')
            ->where('sub_categories.category_id = ?', $this->_catalogLayer->getCurrentCategory()->getId())
            ->where('e.entity_id != ?', $this->_catalogLayer->getCurrentCategory()->getId());

    return $collection;