Maybe I'm wrong, but I thought when you ask for a DAS you have to have your entire party with you. If each member of a family is asking for a DAS, and they have to have with them the people they want to be able to accompany them for attractions, I think it would be quite obvious to Guest Relations that these people are trying to cheat the system.
I have friends who require a DAS for each member of the party, partly because they split up sometimes, and partly because they have different needs. They have a genetic condition that the whole family has (dominant) so yep, whole family needs a DAS. But they are worried about going into GR to ask, so they have one right now, for one person, and if they get more, they will get them one at a time - they are afraid of people faking or exaggerating and making them look bad.
I have traveled in a group where all 3 of us had a DAS, and all for very different reasons (we were not related).