It is best to take out the old tile floor before putting in the new tile especially If your old tile floor is over wood framing,

You are adding unwanted extra weight to the floor structure....and houses in 1925 were not built on concrete slabs so odds are pretty good that you are on a wood frame. .

Also, by adding a second layer of tile over the existing tile, you are raising the floor up and losing head height in the room...........

I would not do it.............

Also, why aren't you putting in new wood flooring instead ? It is so much more pleasant to live on then tile ...........and much more appropriate to the era of the house.

Lampert Dias Architects is right. Absolutely take up the old tile, make sure the sub flooring is in good condition and put down the new tile.

Also if you tile over broken tiles, you risk breaking the new ones. Do it right the first time.