Change list.phtml to Show Products of Multiple Categories in Same Block

Subject is very concise: I need to show all products within given categories in a CMS page.

To accomplish this, I want to change list.phtml, since it's easy implementable and have a cool appearance.

To be more clear, I want my block like this:

{{block type="catalog/product_list" name="product_list" category_id="12,13,26" column_count="5" mode="list" template="catalog/product/multiple_list.phtml"}}

Is it possible? I'm trying in several ways, but just can't figure out the logic to use in list.phtml that fit in my needs.

By the way, I've tried these solutions, but they aren't exactly what I'm in need:

• Display more than one category in the same CMS Page
• modify list.phtml to show only a limited number of products on home page
• Show Specific Categories On Magento Home Page

Points of interest:

• Magento version: 1.9.2
• Already showing products of single category
• Listing products of given root category would fit, but doesn't work too (it's showing products of all the other root categories)

Edit 1:
I have found a answer that comes real close to what I need:

<?php
/**
* Displays multiple category view templates along with the product list for it
*/
/* @var $this Mage_Core_Block_Template */

$category_ids     = explode(',', $this->getData('category_ids'));
$current_category = Mage::registry('current_category');

if ($current_category) {
Mage::unregister('current_category');
}

foreach ($category_ids as $id) {

$category = Mage::getModel('catalog/category')->load(trim($id));

if (!$category->getId()) {
    continue;
}

Mage::register('current_category', $category);

$product_list = $this->getLayout()->createBlock('catalog/product_list', 'product_list_'.$id, array('template' => 'catalog/product/list.phtml'));

echo $this
    ->getLayout()
    ->createBlock('catalog/category_view', 'category_'.$id, array('template' => 'catalog/category/view.phtml'))
    ->append($product_list, 'product_list')
    ->toHtml();

Mage::unregister('current_category');
}

if ($current_category) {
Mage::register('current_category', $current_category);
}

The problem now is that this code is showing all products in root category, instead of the products within category given. Yet it's showing all product lists in it's own block. I want to show all three product lists in same block.

Edit 2: Now I've got this:

<?php
/**
 * Displays multiple category view templates along with the product list for it
 */
/* @var $this Mage_Core_Block_Template */

$category_ids     = explode(',', $this->getData('category_ids'));
$current_category = Mage::registry('current_category');

if ($current_category) {
    Mage::unregister('current_category');
}

foreach ($category_ids as $it => $id) {

    $category = Mage::getModel('catalog/category')->load(trim($id));

    if (!$category->getId()) {
        continue;
    }

    Mage::register('current_category', $category);

    global ${"category_"$it} = $this->getLayout()->createBlock('catalog/product_list', 'product_list_'.$id, array('template' => 'catalog/product/list.phtml'));

    Mage::unregister('current_category');

}

foreach ($category_ids as $it => $id) {
        global array product_list ( array $product_list [, array ${"category_"$it}] );
}

Mage::register('current_category', 'category_1');

echo $this
    ->getLayout()
        ->createBlock('catalog/category_view', 'category_1', array('template' => 'catalog/category/view.phtml'))
        ->append($product_list, 'product_list')
        ->toHtml();

}

if ($current_category) {
    Mage::unregister('current_category');
}

This part of code should:

• Create 3 arrays of products
• Merge these 3 arrays into 1 "products_list"
• Create 1 block as "view"
• Echo all 3 arrays into same block.

But now, it just stops my CMS page, breaking all content page.

Edit 3:

I'm not sure about how to create my own block, or how to call a block defined by me, but following @fschmengler and @Wouter Steenmeijer, here's what I have now:

Layout Update XML:

<reference name="content">
    <block type="core/template" name="multiple_categories" template="catalog/category/list.phtml">
        <action method="setData"><key>category_ids</key><val>12,13,26</val></action>
     </block>
</reference>

file: app/code/local/starscream/default/block/multiple.php

content:

<?php
 protected function _getProductCollection()
    {
    $category_ids = $this->getCategoryIds();
    $productCollection = Mage::getModel('catalog/product')
        ->getCollection()
        ->addStoreFilter()
        ->setVisibility(Mage::getSingleton('catalog/product_visibility')->getVisibleInCatalogIds());
        ->addMinimalPrice()
        ->addFinalPrice()
        ->addTaxPercents()
        ->addAttributeToSelect(Mage::getSingleton('catalog/config')->getProductAttributes())
        ->addUrlRewrite()
        ->joinField(
            'category_id', 'catalog/category_product', 'category_id',
            'product_id = entity_id', null, 'left'
        )
        ->addAttributeToFilter('category_id', array(
            array('in' => array($category_ids)),
        ));

        return $productCollection;
    }
?>

I didn't find how to call this "multiple.php" block I created in my CMS page… Am I missing something?

Any help is appreciated.