It is not really a person that gets reincarnated, you are seeing it from a point of view that is clinging to an inherently existing self.
You or I as in the form of our human name, when this life ceases, so too does that person, that form, cease.
What "carries on" is karma.
In this case the proclivity to cling to a self. As well as the proclivities to do X actions, seek desire, seek sensuality, and also results of what actions were created in this form or previous forms, will arise again to "decide" as to where a new form will arise in relation to the previous actions and proclivities.
Now the question you want to be asking as to answer your question is when in the past or in past forms has desire been created and/or has actions been performed where in relation two forms will arise simultaneously.
It is a conundrum, but we can see in some way that things like multiple forms resulting from pervious karma can be possible if only to look at things like twins or multiples human babies being born in tandem. (or other animals that have litters of children)
Or look at people with multiple personality disorder, which could be a result of either multiple forms existing in one human form, or just simply a broken mind with mental formations that are not stable (I know too little of the phenomena to make a biased judgement)
The real wisdom in this is that the Buddha himself would not explain the intricacies of karma simply because it will lead one to ruin. It is unable to be knows.
It is one of the 4 imponderables. So anyone claiming that they Know the answer to your question would be fabricating it of their own as this would have never been taught by the Buddha.
What is and should be more prevalent to you is as to not create causes for future unfortunate rebirth into such a horrid state as well as to create causes for a more positive rebirth and current scenario.
Being overly concerned as to where "I" will end up after the human death experience is just a form of strong clinging, the clinging that is described and explained as the second of the four noble truths, the clinging that brings suffering with it as they are intertwined.
There are specifically 4 (technically 8) milestones where one can say with conviction that you will know where your next rebirth will take you.
Firstly if you committed any of the 5 heinous actions in this life, you will know for sure you will be reborn in a hellish state.
If you reached the state of the fruit of sotapanna, after your experience of nibbana you will know for sure you will be reborn in a form conducive towards leading to liberation.
If you reached the state of anagami, you will know for sure you will be reborn in a pure realm and never have to come back to a human form.
If you reached the state of arhant you will know that there will be no more rebirth for you at all, as there is no you to be reborn and no more causes created that will cause a rebirth.