Is there a way to install a new floor over cracked ceramic tiles?

Depending on what you want to put on top, it is a big maybe. Think about it for a minute. You are now adding to the height of the floor, now creating a lip or awkward transition from one room to the next - creating a tripping hazzard. Next your floor is as only as good as the sub floor. If your current floor has cracked or broken tiles, that tells me that they were poorly installed or that there is a problem with the sub floor beneath the cracked and broken tiles. Until the subfloor is properly fixed, anything you put on top of it will fail in the short term. My vote is to wait and pull all the old flooring up, repair the sub floor and replace with new. I hate to see you throw you hard earned money away unnecessarily.

No! Any problems with the existing floor will transfer to the new flooring. Needs to be removed.

Both of the comments about the subflooring issues may be correct. Have you considered putting some levelling compound down and then covering it with vinyl?

LOWES sells an incredible product SMARTCORE vinyl planking that floats and we have laid over large cracks in concrete floors without any issue.

I used groutable peel and stick tiles 12" x 24" in my bathroom. After grouting, you couldn't even tell they were vinyl - looked just like travertine.