My client was having trouble with duplicate orders that had the same order ID in the Orders view. The receipts would have an order ID with a suffix "#1" and "#2". If the order had two products, the products were split between the orders. The payments weren't split, there was just one transaction.
In this case it was caused by the advanced stock management. It seems that a product MUST be assigned to a stock, or otherwise no delivery method is available at the cart.
ANYHOW, if you add two products in cart where the other product has been assigned to a stock and the other one is not, it was possible to finish the order, but the products were split to two orders. I assigned all the products to the main stock with CSV, and everything seems to work now.
I wanted to share the problem I had if it helps some other people too. Prestashop version is 1.6.1.9.