We successfully got our second passports for vacation travel to Mexico when we could not get the first ones back from the third world country’s embassy that unexpectedly shut down because some big wig leader passed away or something like that (long story). IIRC, we did not need the actual first passports, but we had to show up in person at the passport office in Seattle.
We needed our IDs, proof of citizenship, affidavit that our passports were in a “black hole,” photos, a large fee, proof of travel to Mexico, and application forms.