For those who want to follow the path of an amended return through IRS, it’s all in the Internal Revenue Manual and you will learn that there’s not much difference between electronic and paper returns. The key question is whether your claim is a CAT-A.

What’s a CAT-A? It’s one that requires a closer look by a tax examiner. And IRS is not going to tell us, what they are looking for. That’s why that part of the Manual is X’d out. See

https://www.irs.gov/irm/part21/irm_21-005-003r#idm140006922960688

What the Manual does tell us is that the person making the CAT-A call tells the examiner how the return was sent:

“If referring a MeF amended return meeting CAT-A criteria, include in your remarks 'MeF Amended 1040X', to indicate that the amended return documentation can be reviewed via the MeF Return Request Display (MeF/RRD) application.”