To add a new recording over previously recorded material. A noun or pronoun can be used between "dub" and "over." If that part of his vocal is garbled, we can just dub it over with a section from a different take.
dub something over
to record a replacement sound over another sound in a recording. They had dubbed over all the dialog in the movie. It doesn't matter if you say a word wrong on the tape. We can dub it over.