You can *both* SDC together by calling 24 hours before the departure of the first original flight; the new flight(s) can be anytime during the same day. You need two coach seats in the same inventory class and there's a fee (IIRC $75 each unless each has high enough DL status).

If you try to change earlier, there could be a fare difference and you both need to be rebooked together and in an inventory class that allows use of the companion cert. If this is the return portion of the RT, it could be easier. AFAIK the cert itself doesn't have an advanced purchase requirement or other restrictions but some of the applicable fares do.

You could also try to make the changes yourself on the DL app, but be careful about whether you're doing a SDC (normally done during OLCI) versus simply changing (DL might call it modifying) flights.