Step drills sharpen perfectly on a lathe, but not everyone has one, and paying a turner for such work is unprofitable. If in the workshop there is only emery, then the drill can be corrected on it. However, the specificity of emery allows you to do this only by regrinding the cutting edges in a new way, which, however, is not difficult.
Stepped drill sharpening process
Sharpening on emery is carried out from a smaller diameter to a larger one. The blunt edge of the drill is applied parallel to the working surface of the abrasive disc. The shank should be slightly below the tip.
When removing metal, you must first grind off a regular smooth transition to a step, and then select it so that the cutting edge protrudes above the part of the drill behind it. In fact, you need to achieve the same effect as on a conventional twist drill.
If there is no experience in sharpening even ordinary drills, then it is worth checking the operation of the drill after the first diameter to make sure that the angle is correct. When the restored part starts to drill properly, you can sharpen the rest of the worn steps by analogy.