<?php

$productClone = $this->objectManager->create('Tx_Theext_Domain_Model_Product');

// $product = source object
$productProperties = Tx_Extbase_Reflection_ObjectAccess::getAccessibleProperties($product);
foreach ($productProperties as $propertyName => $propertyValue) {
    Tx_Extbase_Reflection_ObjectAccess::setProperty($productClone, $propertyName, $propertyValue);
}

// $productAdditions = ObjectStorage property
$productAdditions = $product->getProductAddition();
$newStorage = $this->objectManager->get('Tx_Extbase_Persistence_ObjectStorage');
foreach ($productAdditions as $productAddition) {
    $productAdditionClone = $this->objectManager->create('Tx_Theext_Domain_Model_ProductAddition');
    $productAdditionProperties = Tx_Extbase_Reflection_ObjectAccess::getAccessibleProperties($productAddition);
    foreach ($productAdditionProperties as $propertyName => $propertyValue) {
        Tx_Extbase_Reflection_ObjectAccess::setProperty($productAdditionClone, $propertyName, $propertyValue);
    }
    $newStorage->attach($productAdditionClone);
}
$productClone->setProductAddition($newStorage);
// This have to be repeat for every ObjectStorage property, or write a service. 
?>

You need a copy of your model and relations (ObjectStorage properties).
In this example there is a model Product with property ProductAddition (1:n relation).

Extbase: Make a (deep) copy of the model

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