Does depend on the fare rules involved when you purchase the ticket. They will explain the ability (and cost) of changing dates. Some fares are 'companion' fares, and require both parties to fly the same flights - but Cathay doesn't really use this type of fare.
Just because two people are on the same itinerary doesn't mean they have to fly the same flights, although the online booking system on the Cathay site doesn't have that sort of flexibility to book online, and it would have to be booked through a travel agent or Cathay by phone.
The other option is to purchase the tickets separately and then assign seats next to each other on the flights (and perhaps get Cathay to link the two tickets).