The phrase "on top of each other" is commonly used to describe objects or people stacked or piled one above the other. However, there are several synonyms that can be used to convey a similar meaning. For instance, the phrase "stacked up" implies that one object is placed directly above another, while "heaped" suggests that multiple objects are piled together in a disorganized manner. "Layered" can also be used to describe objects arranged one on top of another, while "overlapping" implies that parts of each object are covering those beneath them. "Jumbled" and "crowded" are other synonyms that can be used to describe a similar scenario where things are closely packed or piled together.