If you are talking about having one room along a side of the house have screens (and just one wall with screens) instead of windows, my parents had a porch like that. You will not get much fresh area flowing into the porch because with three solid walls you won't get a cross breeze. A screen porch works best, in my opinion, if it has screens on two walls so that you can get a cross breeze. My parents ended up converting that porch to a regular room and adding on a conventional screen porch that had screens on 3 sides. If you do it, make sure that you have adequate overhangs over the screen and that the floor slopes slightly to weep holes for the water to drain out as you do not want to have standing water from rain storms, snow melt, etc. in a room over a basement.

I can think of a couple of possible issues.

One, the area above the porch will be more difficult to heat and cool.

Two, if you are going to have multiple entrances and windows to the porch from the various rooms, it will make something as small as a 10x12 porch less usable, just from having less wall space. Also, you are creating a situation where there are windows from a private area like a bedroom into a public space which is going to function more like an outdoor room and less like a traditional porch. This might not be an issue for you, but the diminished privacy should be taken into consideration for your own comfort level and when choosing window coverings.

Thank you both for pointing out things I wasn't even thinking of. Anything that could casue issues, I will stay away from. It looks like we will put the screened porch in the back corner like we originally had planned. Thank you so very much for helping me! Take care!!