We are a group who have booked tickets together, and now one of us needs to change their ticket. Can we change one ticket while the others in the group travel together as planned?

No, unfortunately not. When the tickets are linked to the same booking reference, changes can only be made that apply to the total number of passengers.
If you want to be sure to have this kind of flexibility, so that each of you can make changes to your journey individually, you should book separately in the future.