It's exactly as
@Stuart ********
's stated. There is no official limit on the number of "piggy back" (dependent) visa/extensions that can "cling-on" to yours. Your wife and children can indeed get Non-O visas and then yearly extensions based on yours.
Now with that being said you need to talk to the university BEFORE you wing your way here because you're better off with everyone getting the correct visa before you show up here rather than comin' in on tourist visas and trying to convert the inside the country. You would get a 90 day Non-ED visa, your wife & children would get a 90 day Non-O visas.