With that
TSC bag in the photo you are in the US, but where? What kind of weather will you have? How big is that area under there, in feet? Length and width? Do your chickens free range or will you have a run?
What is in the barn behind it? Is it pretty air tight or well ventilated? Would it matter if the stuff in it got dusty from chicken dust? Some more info could help.
My first observation is that rain will come off the front of that barn. If you have a run in front of it that water will get it wet. If the water runs back underneath that overhang your coop can get wet. If you have a door under that overhang you'll get wet going in and out. A gutter and downspout might be a good investment. I'd consider building up the dirt level under the overhang so water doesn't drain in there. I did that with my coop and it worked well. The coop stays dry.
If the stuff in the barn can handle the dust, I'd cut some big holes high in that wall and cover it with hardware cloth to give great ventilation in the new coop. It will be protected from rain and protected from wind. My coop is the end of a shed. When I closed it off I left the top open with hardware cloth for predator protection. Worked great.
I had a door where I could go from the shed to my coop. You could try that with your barn. That way I can walk into the shed without water pouring on me if it is raining and I can store feed in a metal garbage can in the shed. It gives me good dry access to the chickens and room to store things.
will they deal with a dual level nesting area ?
Depends on how you build it but yeah. You have Brahmas so you know they are not helpless. With a little motivation they can get around.
I'd also like to repurpose what we have
What do you want to use that small coop for? Any plans?
Without knowing how many chickens or what size that is, my general thoughts are to move that old coop out in front and box in the entire overhang. Depending on where you are that may be with plywood or paneling or maybe some of it wire. Then build a run out front that encloses the old coop. Section off a part of that run so it can be isolated around that old coop. That would give you a good place to house the new chicks to help with integration and a good place to isolate a chicken if you need to.
