Do I need to have all my passports with me for green card application?
Since the current passport has the latest visa, I suppose it would suffice BUT you need to have the old one handy as it links you to your first visa. If you are a fan of spy movies you will know there are aliens and foreign powers that plant sleeper agents by systematically replacing locals with clones. Keeping all your old passports is an easy way to prove you are the original you.