Really? The t&c are clear?

Daily complimentary full breakfast inclusive of one entrée (or standard breakfast buffet), juice and coffee (tax, gratuity and service charges included) will be provided to the member and each registered guest in the room, maximum four (4) people when staying at Hyatt Place properties, Hyatt House properties, or Hyatt Residence Club resorts.

It mentions a max of 4 people only at Hyatt Place, Hyatt House to Hyatt Reidence Club resorts. Otherwise it only mentions registered guests.

It seems clear to me that other Hyatt, Grand Hyatt and Park Hyatt properties are not constrained by the 4 guest limit, as long as they are a registered guest.

I've never had a problem getting benefits for an additional room.

One thing to do when booking award rooms is to book to the maximum allowed occupancy. This way, if they refused breakfasts/club access on a second room, you'd have more people registered in the first.