No, while you are on a ride you cannot check in for another ride.
When you have claimed back-to-back rides, you will be able to check in for the second ride once the first ride is complete. If the first ride ends less than 60 minutes before the second ride begins, you have a 5-minute window to check in for the second ride after completing the first ride.
Your earnings for the second of two back-to-back rides are protected from the time you check in for the first ride. Learn more about fare protection for back-to-back rides in this article.