I have been getting this error when trying to filter a products collection

Item (Mage_Catalog_Model_Product) with the same id "7631" already exist and wanted to ask what could ne causing the error since there is only one (visible) product with the same ID inside of Magento.

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Here is the solution i did to solve the issue.

This works on arbitrary collection, not only for Catalog_Model_Product.

Step 1. Modify the core file lib/Varien/Data/Collection.php, function addItem(), but unlikethis answer suggests, don't hide the error.

Instead, add extra error information to the exception thrown:

        if (isset($this->_items[$itemId])) {
            throw new Exception('Item ('.get_class($item).
                ') with the same id "'.$item->getId().'" already exist' .
                '. SQL that caused this: ' . $this->getSelect());
        }

Step 2. Take the offending query from your error report and run it by hand. See what records duplicate the collection key. Add order by <key field> as needed.

Dissect the query removing the participating tables one-by-one, and see which record caused the duplication.

In my case it cause by my product collection returns duplicate product ids, so i grouped my product collection by grouping 'e.entity_id'

Here is my sample code

<?php $collection = Mage::getModel('catalog/product')
->getCollection()
->joinField('category_id', 'catalog/category_product', 'category_id', 'product_id = entity_id', null, 'left')
->addAttributeToSelect('*')
->addAttributeToFilter('category_id', array('in' => $uniqueIds)); ?>

<?php $collection->getSelect()->group('e.entity_id');?>