Check, check, check, and check.
First, two people, for Jan 4-10
Second, two people, for Jan 4-10 with new flight numbers
Third, four people, for Jan 2-10, two different airlines, different arrival times, and now, two reservations which aren't linked for dining reasons
Fourth, four people, for Jan 2-10 and more new flight numbers
Unfortunately, it's taken more than four calls because on the third step, the CM completely ignored what I was telling her and only scheduled one of the three flights she needed to do. At least it's all straightened out now!
Everyone's responses have been really helpful. Thanks

I'm definitely going to bookmark this for the future, and hopefully I never need to reference it again!