Topps did this starting in 1958. They included the next series checklist in the previous series (starting in 1961 but on the team card backs for the 3 years prior) and then there were either 11 or 22 cards from the "next" series on the sheet. A little enticement to get the kids anticipating the next series. The practice of lagging did not end until 1966.
I cover some of this on my blog (short version):
https://toppsarchives.blogspot.com/s...l%20Checklists
Long version:
https://toppsarchives.blogspot.com/s...t%20Relativity
I believe in 1958 Topps sold six series using only five press runs using this method. I also think they only put together the last series after signing Musial. (EDIT 9/10/23: It was six press runs.)