I don't know how a 'mainstream' Buddhist would answer this question
What does scripture say?
Inventing an answer is the same as stating falsewitness.
What is reincarnating then?
If, theoretically, All matter & energy & All space and time is capture and held in the palms of one's hands ---we can say that ALL IS ONE.
This ALL IS ONE is an absolute.
This absolute would hold all possibilities. It would be the absolute Truth.
The Absolute truth stands in contrast to in-absolute transiency.
NO TWO bits or specks of anything can occupy the same time and place at the same time ---this is an absolute law of nature. If we could spread a grid over the entire cosmos ---we will see that each and every point of existence is individual & seperate from each other & occupy a bit of space all its own.
All is false because all is transitory ---but all is actually transpiring during a passage Real time. The falsity is that the state of existance is transitory and made of in-absolute matter & energy that is stagnant until a conscious overseer passes by.
When a conscious overseer passes by, time is seen to flee and when a conscious overseer passes from living body it appears that there is no more "time" for the dead body to live ---yet time and life continue.
Consciousness is above Time, death, space and transitory forms ---yet, birth in a body allows the life-force to interact with matter, while the time affords its panoramic vision to tickle itself.