The video below details how to connect MemberPress to Invoiced.com using Zapier and MemberPress Developer Tools add-on.
This does require MemberPress Plus or Pro edition, an Invoiced.com account and a paid Zapier account.
The steps in this video could possibly be applied to other invoicing services that support Zapier also if Invoiced.com isn't quite the right fit for you. But you'd have to do some trial and error to get it working with something else following the same procedures found in this video.