Automation rule to update already integrated records

Currently, automation rules provide the ability to send an Aha! record through an integration based on the record being updated in a specific way. We would like for the ability to push updates to already integrated records in the same way. This is because in certain cases we need an update received from one integration to impact another integration. An automation rule seems like the easiest way to do that today but updating an already linked record is not yet supported.