How to filter collection and still keep the original collection in Magento 1

Question

I've created a custom module that allows you to add custom labels on product page. So I have a collection of custom objects and I want to filter it but I want to keep the original collection too.

This is my code to understand better:

The model:

class Company_ModuleName_Model_Label extends Mage_Core_Model_Abstract
{
    private $_collection;

    public function __construct()
    {  
        $this->_collection = $this->getCollection();
    }

    public function filterByNew()
    {
         $collection = $this->_collection;
         $collection->addFieldToFilter('type', 'new')->addFieldToFilter('status', 1);

         return $collection;
    }

    public function filterByOld()
    {
         $collection = $this->_collection;
         $collection->addFieldToFilter('type', 'old')->addFieldToFilter('status', 1);

         return $collection;
    }
}

And the controller:

class Company_ModuleName_Adminhtml_LabelController extends Mage_Adminhtml_Controller_Action
{
     public function dosomethingAction()
     {
         $model = Mage::getModel('module/model'); //the collection is defined in __construct

         $new = $model->filterByNew();

         //do something with $new

         $old = $model->filterByOld();

         //do something with $old
     }
}

The problem is that after filtering by new, the original collection is not kept. $this->_collection is now filtered by new, even if I put this line $collection = $this->_collection;. So now if I want to filter by old, it returns nothing because it's already filtered by new.

Is there a way to filter the original collection by both types, new and old, but not in the same filtration, without loading the collection again?

Thanks a lot!