You can grind off every single bit but the serial number if you want.I see no reason why not as long as the manufacturer, model number and serial number are still visible. Logo's and artistic engraving are at the whim of the owner.
We talking 80shence the routerIf the obliteration results in the inability of the ATF to trace the firearm to the manufacturer it would be a violation. Sometimes the manufacturer is needed to track it to it's source. Serial numbers are often duplicated from one manufacturer to another due to millions of firearms being manufactured every year it would totally impossible to not duplicate another manufacturers numbers at some point without creating a string of numbers or letters so long it wouldn't fit anywhere on the firearm. I'm sure the ATF has that situation covered somewhere in the regulations.
You would have to apply for a variation as you are still defacing the original serial. Unlikely to be approved, normally only happens if your gun was stolen and the criminal defaced the serial. Then a variation may be approved to have it remarked.I just a thought...What about moving the serial number, say from the left side to elsewhere?
Here is what CFR has to say about it, https://www.law.cornell.edu/cfr/text/27/478.92
(1) Firearms. You, as a licensed manufacturer or licensed importer of firearms, must legibly identify each firearmmanufactured or imported as follows:
(i) By engraving, casting, stamping (impressing), or otherwise conspicuously placing or causing to be engraved, cast, stamped (impressed) or placed on the frame or receiver thereof an individual serial number. The serial number must be placed in a manner not susceptible of being readily obliterated, altered, or removed, and must not duplicate any serial number placed by you on any other firearm. For firearms manufactured or imported on and after January 30, 2002, the engraving, casting, or stamping (impressing) of the serial number must be to a minimum depth of .003 inch and in a print size no smaller than 1/16 inch; and
(ii) By engraving, casting, stamping (impressing), or otherwise conspicuously placing or causing to be engraved, cast, stamped (impressed) or placed on the frame, receiver, or barrel thereof certain additional information. This information must be placed in a manner not susceptible of being readily obliterated, altered, or removed. For firearms manufactured or imported on and after January 30, 2002, the engraving, casting, or stamping (impressing) of this information must be to a minimum depth of .003 inch. The additional information includes:
(A) The model, if such designation has been made;
(B) The caliber or gauge;
(C) Your name (or recognized abbreviation) and also, when applicable, the name of the foreign manufacturer;
(D) In the case of a domestically made firearm, the city and State (or recognized abbreviation thereof) where you as the manufacturer maintain your place of business; and
(E) In the case of an imported firearm, the name of the country in which it was manufactured and the city and State (or recognized abbreviation thereof) where you as the importer maintain your place of business. For additional requirements relating to imported firearms, see Customs regulations at 19 CFR part 134.