Infinite keys... but so many of them aren't worth holding on to. Basically you only need keys that get you breeding components from each family and a Lord key (well... realistically you can get most of the breeding components you need from storyline worlds and anything more important you can just pick up by stealing monsters from enemy masters!).
I wonder if it will be like the old ones? In the old game, I kept logs on graph paper of my keys with notes as to unclaimed treasures (such as dream eggs and more keys) and what monsters the keys had which were good. I used graph paper to make char