I finally ended up inheriting my test class from that class:

<?php

class MultiDomainCase extends TestCase
{
    protected $domain;
    
    public function setUp()
    {
        if (!empty($this->domain) || !is_null($this->domain))
        {
            $configuration = $this->getConfiguration();
            $configuration['url'] = $this->domain;
            $this->saveConfiguration($configuration);
        }
        parent::setUp();
    }
    
    public function tearDown()
    {
        if (!empty($this->domain) || !is_null($this->domain))
        {
            $configuration = $this->getConfiguration();
            
            // TODO revert to initial version
            $configuration['url'] = 'http://localhost/';
            $this->saveConfiguration($configuration);
        }
        parent::tearDown();
    }
    
    private function getConfiguration()
    {
        $configurationFilePath = __DIR__.'/../config/testing/app.php';
        if (file_exists($configurationFilePath))
            return require $configurationFilePath;
        
        return null;
    }
    
    private function saveConfiguration($configuration)
    {        
        $configurationFilePath = __DIR__.'/../config/testing/app.php';
        $content = '<?php return ' . var_export($configuration, true) . ';';
        
        file_put_contents($configurationFilePath, $content);
    }
    
}

The test class would look like this:

<?php

require_once(__DIR__.'/../MultiDomainCase.php');
class DomainTest extends MultiDomainCase 
{
    protected $domain = 'http://some.website.com/';

    public function testDomainHomepage()
    {
        // Given
        
        // When
        $crawler = $this->client->request('GET', 'http://some.website.com/');
        
        // Then
        $this->assertTrue($this->client->getResponse()->isOk());
    }

}

Now I can test my subdomains.