The phrase "piling up" typically refers to accumulating or gathering objects in a heap. There are several synonyms that can be used to describe this action, such as stacking, heaping, amassing, collecting, accumulating, or mounding. These words all indicate the idea of layering or adding objects to a growing pile. Other synonyms for "piling up" could include crowding, clustering, or cramming, which conveys a similar sense of objects coming together in a tight space. Overall, there are many different words that can be used to describe the act of piling up, each conveying a slightly different nuance to the process.