Ah, Moderators...examine the motives of the questioner closely please to see if there is perhaps an under-the-bridge origination. Many thanks.
An answer has been given: Rebirth ends upon Realization of Nibbana. That is the set point; the Limit. The number varies depending on the individual. Since no Beginning point can be determined, because no beginning point of sentience itself can be determined -- Buddha described the beginning point as lost in beginingless time-- there is no place to begin the tally.
However, upon Realization, an individual can supposedly make a survey of all of his/her past existences so if he / she decides to do so, this Realized being could determine a specific number. Though why he/ she would want to is specious.
Hope this helps,
Author of Redneck Buddhism: or Will You Reincarnate as Your Own Cousin?