Since going forward and backward is a matter of perspective, yes… you can do it. It just depends on the intention. If you have the intention to go up the stairs, but stop and turn around, but still have the intention to go up, you are literally standing backwards on the stairs.
Now if someone happens to walk by and asks what you are doing, and you tell them you are going up the stairs, they might ask why you are standing backwards on the stairs.
Another example is an escalator where you can also stand backwards… escalators are literally rolling stairs… (In German)