You can record any book that is in the public domain in the U.S. for LibriVox. Yes, you can do a second (third, fourth, etc) version of a book already in the LibriVox catalog. Books in the Readers Wanted forum are collaborative projects that have been launched as a group project by a someone who then becomes the Book Coordinator (BC) for the project.
However, before you start, please have a look at the
NewbieGuideToRecording if you haven't already done so.
Next, even if you are experienced with recording elsewhere, please send in a short test recording to check that all the technical settings meet LibriVox requirements before recording a full chapter.
1-Minute_Test
Also as a new reader, we strongly recommend that you record a section or two in one of those group projects before embarking on a solo, so that you can get a sense of the amount of time and effort a commitment to a solo recording of an entire book would entail, as well as become a little familiar with the community here and our process for submitting files, prooflistening, etc. before starting off on your first solo project.