How to connect to multiple database via mysqli?

Hello,

I have created a class when I used to connect to the database using the __construct function.  This class also act as my selecting and executing of query.  I get this working for connecting to one database as I define the database host, username, password and db_name as a constant.  Now I want to somehow be able to pass different database name to this class, how can I do this so that this class continue to work?  For example, my constant DB_NAME is "test database".  I want to contact to another database name "test2 database".  How can I make it work?

My code for my class:

**note the upper case name is define in another file**

class QueryBuilder
{
public $host = DB_HOST;
public $db_username = DB_USERNAME;
public $db_password = DB_PASSWORD;
public $db_name = DB_NAME;

public function __construct()
{
      $this->mysqli = new mysqli($this->host,$this->db_username,$this->db_password,$this->db_name);      
}

public function __destruct()
{
      $this->mysqli->close();
}

public function select($sql)
{
      $qry = $this->mysqli->query($sql);
}

public function query($sql)
{
      $qry = $this->mysqli->query($sql);
}

}