If you have an order in Magento and you don't have stock to fulfill the whole order, you can of course create a part shipment in Magento by selecting only products/quantities that you have in stock.  Allowing you at a later date to fulfill the rest of the items on the order as a second shipment.

After each shipment is created (even if it's only part of the order) a shipment will be sent to Shiptheory.  Thus by the time an order has been completed shipped in part shipments, there will be multiple shipments in Shiptheory and multiple consignments with the carrier(s) for that entire order.