To put in a retractable screen such as this Phantom Screens Sureview over height retractable screen from Lowes could certainly be a good idea. This practical Phantom Screens retractable door screen feature self adjust controls which makes it easy to adjust the tightness and the speed with turn dials, thereby getting you a perfect fit. This particular unit can fit an oversized 96" high door and if you need a double door set up then you'll have to buy two of them.
Over at Lowes you can in fact find a whole bunch of exterior storm doors, screen doors as well as these nice and functional screens. This unit comes with a track away system which features a low profile threshold so the current look of your doorway won't be interrupted. You can find these units either in white, brown and almond, and while most people will probably prefer white, there are always some settings where it actually looks better in an off color. If you like the idea of this screen, then you can always go to Lowes and check out their full selection; they have quite a few of these Phantom door screens in various sizes, so measure your doorway carefully, then pay Lowes a visit and check out their collection of screens.
Phantom Screens White Sureview Over-Height Right Retractable Screen
"Self adjust controls let you adjust the speed and tightness of your screen system with easy-to-use turn dials. The track-away system offers the lowest profile threshold maintaining the look of your doorway. Sureview screen retracts easily with a one touch latch. This screen fits an oversized 96" high door. For double door applications, purchase both a white left and right over-height screen with the white over-height double door kit. Sureview screen is covered by a limited lifetime warranty on parts and finishes - excluding mesh. This is a special order sale, and is also available in almond or brown or to fit a standard size door"
Phantom Screens Brown Sureview Double Door Kit
"Sureview double door kit allows you to screen a door up to 72 inches wide. Sureview double door kit is available to join a left and right screen door. Easy to clean. Easy to install yourself"
These doors are from lowes.com