The only thing that will work is to replace them, but, they will do it again, as you have found out. There is a reason, they are cracking. Improper installation. You may want to read this link. https://ctasc.com/expert-answers/why-do-my-travertine-tiles-have-cracks-and-sound-hollow/

That's 'underneath' stuff. That's not tile stuff. Something UNDERNEATH the tile is causing it TOO MUCH stress and the TILE is cracking. Stone has ZERO 'give' to it. It will take stress until one day it SNAPS.

To fix this you MUST remove the tiles in that AREA (ie the ENTIRE KITCHEN) and then have the SUBSTRATE (the thing it is sitting on) FIXED. Yep. That's where you need to go.

If you are on concrete slab then the slab needs to be grown down and then filled and the tiles replaced. If the tiles crack AGAIN in the same areas, then you need to make sure the house isn't sinking or doing something horrible. Doubt it...but you NEVER KNOW.

If this is over wood-joist system (ie. there's a basement or a crawl space underneath) then you have to ensure the floor joists are secure AND you have the correct deflection rating for the thickness of the subfloor. To be clear, structure comes from plywood and NOT cement backer board.

Tell us MORE about your home's situation...we can go from there.

Just be prepared for removing a large portion (an entire room) to get this to work.

Did they use decoupling membrane during installation?

No I do not believe my builder did. Is there anything I can do now?

Answer SJ’s questions

The tile was put directly on the concrete. The house is only 7 years old. We have had an engineer out and it is not a structural issue. The problem is the kitchen, living, dining is one big area that also feeds into the rest of the house that is the same tile. There isn't a breaking point to remove just a section and I doubt I will be able to match the tile from 7 years ago. Besides removing them, is there anyway to fill in or correct that cracks that are there so they are not so noticeable. I will add a few more pictures to understand the layout.

I'm betting your tile were installed directly over a control joint in the concrete, a fatal error. You can tear it out and install Schluter Ditra as an uncoupling membrane, but it is only gauranteed to work laterally, not up and down which is how concrete sometimes moves.

Another case where the tile setter should have told the homeowner/designer "No, we're not doing it like that." and saved them from themselves.

As far as a repair, get yourself a couple shades of color matched wax sticks and go to town.

And there it is. The answer is rip it up to 'correct' the cracking. Or leave it and add matched wax sticks that you use as filler. You will need to keep the colour on hand as your cleaning will need remove the wax over time.

A tile floor is designed to last 20 - 30 years. You are roughly half way through a SHORT time frame for the floor. A quick change for the tile is 15 years. It's the time frame when a tile floor is poorly installed, cracking or lifting.

I would find a coloured filler (as Joseph suggests) and use it for the next 7 years. All the while you will be saving up to remove ($2-$3/sf), correct the subfloor if needed ($3-$5/sf for concrete) and then purchase a new floor ($3 - $25/sf) and then install it ($3 - $12/sf).

The removal costs and subfloor costs are 'fixed' costs. The replacement costs depend on YOUR purchase wish. The INSTALLATION costs are anchored to the MATERIAL you purchase. A floating cork floor = $3/sf for installation costs. A high-end stone tile install = $12/sf for labour/install.

You have 7 - 10 years to save up for the full removal of this floor. Or sooner...if you really hate it.

Thank ya'll so much for your responses. It is greatly appreciated.