Does the FAA have a document that details each step found in a Component Maintenance Manual?
In general aviation and even working in FBOs, I have referenced AC43.13 to approve repairs that the CMM does not cover. These processes and techniques are approved by the Administrator. In general terms, the FAA tends not to tell you how to meet a requirement but rather gives the requirement then the organization has to meet that requirement through a FAA approved QMS. This process is applicable regardless if you are working with the MIDO, ACO, or FISO. In order to get down in the weeds, you would have to be very specific in your question.

Here is the link to FAA AC43.13 for everyone's review.
https://www.faa.gov/regulations_policies/advisory_circulars/index.cfm/go/document.information/documentid/99861

Best,
Mark