You can get a low profile fan that will fit within the space. I have a powder room on the first floor and chose the Panasonic WhisperFit Lite to go there. It fits nicely and is ducted right out the nearby side wall. The WhisperFit is designed with the motor on the inside of the fan, rather than sticking out the top. In my situation the fan was a replacement for an old, LOUD f-fan. I used rigid duct wrapped in foil-faced fiberglass insulation. The Panasonic fans (and maybe other brands) are designed to allow you to mount the body and secure it before the fan itself is inserted into the body. This gives you more room to work. The fan I chose is 60 CFM, if I remember right. In my small powder room, this is enough ventilation that dust will roll across the floor when the door is closed. I installed a timer instead of a switch, which keeps me from forgetting that it's on. If you don't need one with a light, just look for the WhisperFit series. They can be found on eBay. I would assume that you could branch the electrical circuit from the existing fan to this new one for the simplest hookup. Then both would run at the same time.

Thanks all, I finally got access to the condo's message board and got some help from another resident. He said the ductwork was there and said something about a "door" in the fan unit. I poked around inside of it again and lo and behold, a small piece of sheet metal fell off the side of it and there was the duct! The sheet metal piece had a piece of tape on it that I think may have been a hinge, of sorts--so that it would flap open when the fan was on and then fall back over the duct opening when the fan was off to keep drafts out. But a thick coating of greasy dust had kept it from working properly, and also made it hard to see that that's what its function was. The duct opening is only about 1x2", not the big 3" or 4" round opening that I was thinking it should be. It's still not a great fan but at least it's not blowing all of the air right back into the room! And I will have to figure out how to put that flap back on once the weather gets cold, but I have a bit of time before that will be necessary. PS-- no window in that room, unfortunately...

Solar tube to bring in natural light rather than a window? I don't think there is anywhere else to put the shower that size with that size bathroom. You could also try a clerestory window above the shower/linen closet.

We're gutting old 2nd floor bathroom in 1850 house with dormer floor above and then an attic. Bathroom is in center of house with one outside wall but on front. This is historic house so no venting on front. Bathroom 150 sq. feet. with 10 ft. ceilings. How can I vent? Need a powerful fan too. Can anyone help?