Magento – merge guest quote with customer quote(if custommer log in) magento 2 rest api

The function Mage_Sales_Model_Quote::removeItem() expects $itemId as a parameter, not an $item object.

So, your first foreach statement should be:

foreach($quote->getAllVisibleItems() as $item) {
    if(!array_key_exists($item->getSku(),$quantities))
        { $quantities[$item->getSku()] = $item->getQty(); }
    else {
        $quantities[$item->getSku()] += $item->getQty();
        $quote->removeItem($item->getId());
    }
}

This function is available in Enterprise 1.13. It gives the option to delete a quote item that doesn't have an id:

public function deleteItem(Mage_Sales_Model_Quote_Item $item)
{
    if ($item->getId()) {
        $this->removeItem($item->getId());
    } else {
        $quoteItems = $this->getItemsCollection();
        $items = array($item);
        if ($item->getHasChildren()) {
            foreach ($item->getChildren() as $child) {
                $items[] = $child;
            }
        }
        foreach ($quoteItems as $key => $quoteItem) {
            foreach ($items as $item) {
                if ($quoteItem->compare($item)) {
                    $quoteItems->removeItemByKey($key);
                }
            }
        }
    }

    return $this;
}

I assume you add items by posting to

[POST] /rest/V1/carts/mine/items

But you can also post to a specific cart id

[POST] /rest/V1/carts/{{cart-id}}/items

Hope it helps..