How to do a flood simulation without flooding the whole area and covering surface structures (with DEM)?

I have a high resolution DEM and want to do a flood simulation starting at a river. My hope is that the water runs into historical (now dry) river channels (in which I'm interested in) at first and step by step. In my imagination the whole old channel system appears at the end. But the problem is, the higher the water raises the area which is covered by water gets bigger and bigger. Like in this pic (on the right):

But I would love to get a result like on the left side. Now I hope i can describe this understandable: My idea is to do a flooding step by step and every step will be "saved". At the end you have several flood phases which you can intersect.

Red, green and yellow are the different flood phases and the brighter blue is the intersection. I dont know how to manage this (even after internet research) or if it's realizable at all. Maybe you have an idea or even a better problem solution!? I use ArcGIS with extensions.