[rif]

I know this isn't ideal

But could I lay larger size tiles on top of the existing stuff, which is the quarter sized square format?

Why? I've heard its a PITA to get the old stuff up, and this is for a tiny bathroom.

[Ice10]

A couple things that come to mind, and this may not be the case, but thresholds can get wonky and countertops and toilet seats get lower as the floor surface rises.  Is it a rental? Maybe okay.  Your home? Hummmmm...

I don’t know the room but I’d likely bite the bullet and remove the old tile. Especially if it’s a small area.  Just my $0.1

[Rusty Jefferson]

I just watched this video a couple hours ago. It may be useful. (?) I'm just learning about Schluter. Apparently, you can use the thin Kerdie Board over existing tile, then add the new tile.

https://youtu.be/9kwrCJPREJE

[Early B.]

I know this isn't ideal

But could I lay larger size tiles on top of the existing stuff, which is the quarter sized square format?

Why? I've heard its a PITA to get the old stuff up, and this is for a tiny bathroom.

I have the same issue. I like the Kerdi Board option.

[WGH]

I have been working on custom homes for 45 years. I hate it when there is a level change between surfaces. It's just so tacky and you know the person who did it didn't care, no pride of workmanship at all.

When remodeling my house I asked the tile setter if I should remove the 1950 vinyl (asbestos?) bathroom floor tile before installing porcelain tile. He said yes but leaving the black glue residue is OK.
I used an old iron to heat the tile/glue and a stiff putty knife, it went well but slow. The wood floor and new ceramic tile joint is perfectly level. Time well spent.

[rif]

I didn't see kerdie board being being used on floors, except in shower stalls

DITRA was used on bathroom floors, that might be more appropriate.

I am concerned about height differences at the toilet and transition at the door.  Toilet may be a non-issue since I'm replacing it.

[Bizarroterl]

There are 2 ways to do any job.  One of them is to do it right.  The right way is to pull up the old floor and lay the new floor.

[Ice10]

There are 2 ways to do any job.  One of them is to do it right.  The right way is to pull up the old floor and lay the new floor.

 

[Doublej]

Could you get away with putting linoleum on top of the tile?

[TomS]

My first thought is same as others, it's small space to demo, just do it right. On the other hand, around here people lay the new breed of luxury vinyl plank (CoreTec LVP) right on top of all kinds of substrates - tile, concrete, old vinyl, etc. As long as it's flat it seems to work ok, plus it's water resistant or even water proof.

[Scott F.]

Removing the tile is easier than you think. Run up to Home Depot and rent a small chipping hammer. Get two bits, a 3" or 4" chisel and a 1" chisel. Assuming you have a moderate sized room (say 12x12), it won't take more than an hour or so to get the tile up. You'll want eye, ear and eye protection. It's noisy, dusty and crap files everywhere. Oh, be sure to block off the door opening with plastic sheeting to keep the dust from migrating into other areas of your house. Same goes for HVAC vents. Block those and turn off the unit until you are done so you don't suck dust into your unit.

Under the tile, you'll likely find whats called thinset. It's a lightweight concrete/mortar used to make a level surface to bed the tile. When you chip the old tile out, some of the thinset will come up. No worries. You'll need to trowel down a new layer of thinset before you place the new tile. Once that's done, then you can start setting the new tiles. 

I'm sure there are plenty of YouTube vids to help guide you.