Tiling outdoor steps

[Jimk]

Hi all,first time posting,I am looking for advice,I am tiling my daughters front steps on her house the steps currently have quarry tiles in reasonable condition ,none loose just a couple cracked,I was going to tile directly over them after cleaning and priming,my question is this,the bottom step tiles don't go all the way down to the path ,look to be on a concrete plinth of some sort,can I use my tile adhesive to fill out the front face of these tiles,for a more pleasing look?I don't want to lift these tiles as they have been down a long time and I think it would make more trouble than tiling over,house is about 100 years old,what does anyone think,I am going to use mapei flexible exterior grout,apologies for long winded post,cheers