Become an obsession with and Possess

Possess and become an obsession with are semantically related In some cases you can replace term "Possess" with "Become an obsession with", this words are similar.

Possess verb - To keep, control, or experience as one's own.

Become an obsession with and possess are semantically related in eat someone up topic. You can use "Become an obsession with" instead a verb "Possess".