It is fine to tile over tile, in fact you should have a good level surface to work from, making the installation a bit easier, but here are a few good ides to consider, any broken or loose existing quarry tiles should be stuck back down first, when laying the new tiles on top of the existing ones, start of with a dry run, I.E. do not apply adhesve. Lay the new tile not to fall in line with the existing mortar or grout joints, try using a different size tile, this will also make the project easier, once you are happy with the layout of the first step, just dullicate the process for the remaining ones. There are many good tile adhesives on the market today, just find the right one for your application.
You have not mentioned about the riser part of the step being tiled, if you intend to tile the riser too, take into account the overlap that will required on the step. I hope this information shall be of benefit to you, and good luck with the project. If you do not have a ... more.
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