In addition to accepting or rejecting a candidate arrive at time r, we may consider purchasing an option at a cost cx to recall the candidate at time r+x, but this privilege may be invoked only once. For large sample size, using the best-choice criterion and deducting option costs, the optimal strategy and return are obtained.
Rose, John S. 1983. "The Secretary Problem with a Call Option." E.C.R.S.B. 83-8. Robins School of Business White Paper Series. University of Richmond, Richmond, Virginia.