Empty the file cabinets and take out the drawers. Steelcase file cabinets have a number of tracks for each drawer, and you need to make sure that the drawer is free on each layer when you remove it from the tracks. Set the drawers and all files aside.
Stack the empty file cabinets on top of each other. Ideally the bottom file cabinet should be smaller so that the one on top has more of a base. Line up the backs of the file cabinets against the wall and make sure it's the arrangement you want for the cabinets.
Place a 90-degree bracket so that one side of the bracket is against the side of the top file cabinet and one side of the bracket is against the top of the bottom file cabinet. You need at least one bracket on either side of the top cabinet. Mark with a marker where the holes in the bracket go and set the brackets aside.
Drill holes in both of the filing cabinets where you marked them for the brackets. Once the holes are drilled, line up the brackets with the holes and put bolts through them. Screw nuts onto the bolts on the inside of the file cabinets to hold them together.
Put the drawers and files back into the steelcase file cabinet.