Whether an invoice should be matched against two documents or three is a property of what was bought, not a setting to apply across the whole ledger. Services have nothing to receipt, so two documents is all there is. Goods do, and leaving the receipt out removes the only routine evidence that anything actually turned up.
Configure it by category
Goods to three-way, services and subscriptions to two-way, with a rule that decides from the purchase rather than from the supplier. A system supporting only one is forcing a uniform answer to a question that is not uniform, and the usual result is that goods quietly get the weaker control because it is easier to administer.
What replaces the receipt for services
A confirmation from whoever commissioned the work that it was delivered, recorded against the invoice and distinguishable from the approval. Confirming that something happened and authorising the spend are different assertions, and where the same person does both it is still worth recording them as two acts.
Watch for drift
Organisations drift from three-way to two-way for goods when receipts prove hard to collect, and the drift is rarely a decision anybody made. Reviewing what proportion of goods invoices are matched two-way, and why, turns an unexamined default back into a choice. If the answer is that nobody records deliveries, that is the thing to fix.
Questions people ask about two way matching in accounts payable
Can we override to two-way when a receipt is missing?
Only with the reason recorded, and it should be visible how often it happens. Routine overriding is how a control becomes a formality.
Which purchases genuinely have no receipt?
Professional fees, subscriptions, rent, licences, utilities and insurance. Anything physical does have one, even if nobody currently records it.
Does two-way matching save time?
Only by skipping a check. The time saved is at the point of receipt, and the cost appears when something is billed that never arrived.