I was under impression that heir must obtain 10 required objects, but when I reread that rule I realized it doesn't:
"10. Heirs must leave behind 10 items (no more) of a particular type in the house. No items left can be from previous households. These items must be a) created, b) found, or c) given to you as freebies/perks as part of a career or being a Celebrity. None of the 10 items can be purchased or made on the Display Table. Each house must have a unique item type. " Maybe the bolded "you" might change to "household member" to make it more clear.
I started my own Koffi/Hatch decadynasty but won't start the story until I reach first movement and feel comfortable understanding all the rules fully (and see if I can handle that many NPC's). BP is way to difficult for my PC to handle in long run. So far I'm having a blast!