Yes, you can lay tile over existing tile floors (or a backsplash). Although it’s generally best to pull up your old flooring, you can simply place tiles on top if your existing floor is in good condition.
Before you start, examine your tiles carefully for mold, cracks or unevenness. Provided none of these is an issue, you can begin laying your new tiles.
But if this is your first time laying tile — or if you want to ensure that the job is done right — save time by hiring a tiling professional near you.