Answer
The water level will fall.
Work Step by Step
The iron will displace a greater amount of water while floating, on the barge, than when submerged. A floating, supported piece of iron displaces its own weight of water, which takes up more space than the iron piece's own volume. When the iron is submerged, it displaces only its own volume, so the water level drops.
Try it yourself in your kitchen sink, with a deep bowl playing the role of the barge, and many heavy utensils playing the role of the iron pieces.
