Blockchain solves this (not kidding).
You need a document format that each party can produce and consume, a method of sending/receiving them (something email-ish), and optionally an API to access them.
A distributed database is potentially a way to implement this idea: you get a data format, a method of transferring data, and an access protocol but that's so much more complicated than just a normal web API and even if you went this route the model for consensus is off in the case of conflicts.