I do not know of any GLOs that have this process. Which ones do you know of?

For NPC sororities, many have alumnae initiate programs. such as:
Alpha Delta Pi
Alpha Gamma Delta
Alpha Omicron Pi
Alpha Phi
Alpha Sigma Tau
Delta Gamma
Gamma Phi Beta
Kappa Alpha Theta
Pi Beta Phi
Sigma Kappa
Zeta Tau Alpha

These are only the NPC ones that I KNOW OF. There are likely others as well. Check their websites out, some have info directly on them.