Pictures would help if you can. Otherwise more written details. I can't quite imagine what it would look like by your description. Sorry.
I would assume your thinking of putting shelves on the back side of the stairs that you see when walking down the set of stairs towards the basement?
You need to be careful if that is your thinking. Reason is that your stairways are your lifeline to escape the house if there was ever a fire. If there is materials such as cardboard boxes and pine type shelves fastened to the bottom of the stairs located above and a fire did break out, your adding fuel to the fire that will burn out the stairs quicker. If the overhead stairs are finished over with drywall, you can do this project, but you lose valuable space you were thinking of using.
Also you need to understand that if storage begins to fill the steps you risk these products falling off from the vibration caused when walking on the steps above. When this happens if someone is walking on the stairs below a can or jar could hit them in the head. Not a great way to start the day.
Personally I would figure out some other way to create a storage area there are just to many negatives that risk your safety involved in this type of project. And of course this is assuming I am correct on what your trying to do.
You can however remove the drywall on the side wall and install small shelves in this location, just be sure to put some sort of tiny door or small board across the front to prevent vibration from walking any heavy jars or cans off of these shelves as well.
This sounds like a custom job, without a photo or more details we'd be remiss in advising you. Sorry!