Noting the difficult subject matter of the trial, both the prosecution and the defense asked a judge in Paterson if they could try for a pool of 16 jurors in case some drop out.
Fifteen jurors have been selected so far. Opening arguments are expected as early as Thursday.
The man's former wife has testified at a hearing that he held apocalyptic visions and wanted to create "pure" family bloodlines. She also said he enforced his will with beatings and other forms of punishment.
The man and his wife are not being identified by The Associated Press to protect the identities of their children.