Appends line items to an existing invoice WITHOUT modifying or deleting its other line items (unlike PUT /api/Invoice, which replaces the full line item collection). Each line item may optionally link uninvoiced timesheets, expenses or a fixed amount via TimesheetEntryIDs / ExpenseIDs / FixedAmountIDs; quantities, prices, descriptions and taxes are calculated from the linked records unless supplied, and the linked records are marked as invoiced. The request is atomic: if any line item or link is invalid, nothing is added. The invoice must not be Void; totals, balance and status are recalculated (e.g. a Paid invoice becomes Partial when its total grows).