We are going to tile over an existing tile shower floor, how can we extend the existing drain so its more flush with the new tiling?

Any chance you can post a picture or describe the current drain. Just a side note, it is not recommended to tile over tile. Is there a reason you aren't taking uo the old tile and grout?

We are going to tile over an existing tile shower floor, how can we extend the existing drain so its more flush with the new tiling?
We are going over the existing tile because we can't get it up and we're kind of in a time crunch. Right now we can't even get the drain plate off. The original tile was installed on a what looks like a 4"-5" concrete step ( in the basement on concrete floor). My guess is the drain is in this raised step.

If there is absolutely no leakage happening now you could jury rig a drain extension once you get that drain plate off. Stick needle nose plyers into the grid and squeeze while twisting down with the handle, you can't reuse that piece anyway. Once it os off you can insert a short piece of PVC to extend the drain and attach the new drain screen to that. This is not how oplumber would do it but considering how much you need to raise the drain it should work. Remember that I said absolutely no leakage problem is a must.

That should work. Thank you so much will let you know how it goes.

You might want to window shop at the home center for a shower drain designed to be glue to 2" PVC. The extension collar might just fill your gap.

Suggest you remove the strainer and post a picture. For some reason this sounds like kind of old work. Probably has a copper drain, be kind of hard to add an extension.