If you mean "to own" or "to have" something:
* Own: This is the most direct and simple alternative.
* Hold: This implies a more temporary or conditional ownership.
* Control: This emphasizes power and authority over something.
* Be in possession of: This is a more formal way of saying "possess."
If you mean "to be influenced or controlled by" something:
* Be consumed by: This implies a strong emotional attachment or obsession.
* Be haunted by: This implies a negative or troubling influence.
* Be gripped by: This suggests a strong and powerful influence.
* Be taken over by: This implies a loss of control or agency.
If you mean "to have a particular quality or characteristic":
* Exhibit: This suggests a more visible or demonstrable quality.
* Display: This implies a deliberate showing of a quality.
* Incorporate: This suggests that the quality is an integral part of something.
The best alternative will depend on the specific context and the nuance you want to convey.