An exercise machine that can fold up for storage in a closet, provides a complete set of different exercises, and allows change-out of different types of engines including weight stack or weight engines and extension engines where one or more elastic members is extended such as a bungee engine. The present invention can be supplied fully cabled so that no cable installation is needed. The lower frame can be assembled by pivoting into place and can be secured with fasteners or at most two bolts. The press arms and other features can also be secured with fasteners or at most two bolts. The bottom seat/back seat can be pre-assembled and easily removable. The weight stack or bungee rack can be removed and changed or re-installed. All parts can be held in place with either fasteners or a small number or easily removable bolts.