Um, you may as well just build a new coop... 3x6= 18 square feet... That would be 4 LF or 6 bantam sized... and leaves 2sq feet left over for food and water for winter, and nest box...
Good rule of thumb, 4 square feet of unobstructed floor space per bird. You can get away with less than that, but come winter when they are cooped up more, you will find problems occur because they do not have enough space. Run space, if you are not free ranging, is 10 sq feet per bird. Again, these numbers are for the birds happiness and well being. Less space causes more issues to arise. Pecking order problems are more likely to occur when the space becomes limited. For 6 LF (large fowl) chickens, you really need to have a 4x6 coop, with external nest boxes... Or 4x8 with internal nest boxes. That gives you enough extra space inside to still leave plenty of walk about room in the winter, nest boxes, and food and watering station inside. Then off the front of the coop, you can build a walk in run thats 8x10, This will give a little extra room. AND wood 2x4s and 4x4s come in those lengths... Cuts down on cutting time. HEHEHE.
I built a 8x4 coop. I house 4 large and 2 bantams, and 3 babies right now. Mine however free range ALL year, with a protected run from the winter elements if they do not feel like going out. This year, they were out, even in the snow, and only stayed in the winter run if the wind was up high. Anyway, the initial coop cost less than 200 to build, and I used all new materials. It is up off the ground 2 feet. Stand 6 feet tall. My doors to the coop are on the broad side of the coop so I have no problems reaching in at any point. My birds are very comfortable in it.
The coop you have now, I like it, it is a perfect coop for a small backyard flock. All its missing is wheels to move it around the yard easier.