Approvals already exist in every contractor; they just live in people's heads and inboxes. Writing them down as rules makes them consistent and lets the system route work to the right person instead of the loudest inbox.
Good rules are specific and boring. Invoices that match their PO and receipt within tolerance go to the PM for a quick check; invoices that exceed the remaining commitment go to the PM and the project accountant with the difference highlighted; change orders above a dollar threshold need the project executive. Each rule names a condition, an approver role and what evidence must be attached.
The other half is the audit trail: who proposed what, who approved or rejected it, when, and what the record looked like before and after. That history is what lets you answer an auditor, a surety or an owner without reconstructing a month of email.
Start with the decisions that cost the most when they go wrong: payments beyond commitments, change orders, and changes to the forecast.