The phrase "possessed by me" can be substituted with a variety of synonyms depending on the context. For instance, one could use "owned by me," "belonging to me," or "under my control." Other options might include "at my disposal," "in my possession," or simply "mine." These alternatives can help to convey a sense of ownership or control over a particular item or even a state of mind. For example, one might say they are "consumed by" or "obsessed with" a particular interest or idea. Overall, there are many ways to express the idea of possession, and choosing the right synonym can depend on the tone and context of the sentence.