Nothing about adding up breakers in 408.
III. Panelboards
408.30 General. All panelboards shall have a rating not
less than the minimum feeder capacity required for the load
calculated in accordance with Part III, IV, or V of Article
220, as applicable.
Informational Note: See 110.22 for additional requirements.
408.36 Overcurrent Protection. In addition to the requirement
of 408.30, a panelboard shall be protected by an
overcurrent protective device having a rating not greater
than that of the panelboard. This overcurrent protective device
shall be located within or at any point on the supply
side of the panelboard