I am unsure if the structure of the universe allows it. Too bad we can't devise an experiment to investigate.
Personally, no. When I hear most people explain the logic behind their experience, it makes even less sense.
I find it hard NOT to believe in past lives. There is more evidence it exists now then ever. Like the 4 year old boy who can recount every detail of growing up in the 40s and dying in a WW2 fighter plane. Or the history of the lamas in buddhism that can tell the names and places of their next life before they die. Even in parts of Asia where they put paint on the body of the dying person and then a child is born with a birthmark identical to the paint marking in the same place on the body. If energy cannot be created or destroyed then all the souls from everyone in history are just waiting around bored somewhere? Thinking logically that sounds more farfetched to me than reincarnation which is believed by many different cultures and religions throughout history.
I cant say I believe it but I do have an open mind.