Hi. My name is David and this site is fantastic!

I got a lot of help on it in 2004 for my first tiling project, which was tiling over my 1970's brick fireplace and wall-to-wall hearth. It came out better than I could ever have imagined!
I'm now about to remodel my small (5' x 8') hall bathroom and I need help again. I need to know whether I can (or should) tile over my tiled floor in my bathroom. I've included pictures. The floor is now covered with 1/4" thick ceramic tile. I'm going to use 3/8" thick porcelain tile in my bathroom now. The tile on the floor is solidly attached and has no cracks. The subfloor is 5/8" thick plywood. There is a mud bed that appears to be 7/8" thick. There are a couple of squeaks when I walk on the floor (no noticeable bounce though).
Can I tile over the existing tile? If I can, do I roughen up the tile (how?), apply modified thinset, and then tile? If I shouldn't tile over the floor, will the mud bed underneath get ruined when I remove the already attached tile or do I have to remove the mud bed as well and add more plywood (how thick?) and cement board (how thick?) on top? I already own a rotary hammer and a flat chisel for it, if that will make the removal not a big deal.
How should I handle the transition to the marble threshold? The existing marble threshold is 3/4" thick. The new tile placed on top of the existing tile is flush with the top of the existing marble threshold. How thick will the new thinset add to the height?
Thanks for reading through all my rambling! I think I have a better handle on replacing the existing tiled tub surround than what to do with the floor!