Can a stepmother or stepfather apply for immigration for a stepson?

Yes, first, the stepfather/mother should provide the divorce certificate and the current marriage certificate (both of which need notarization).

If you want to apply for immigration for your stepson/daughter, you need his/her biological parents' written consent (notarized).

If the custody of the child belongs to the other party, it needs to be changed in writing (notarized)