Hey there Gogetama2,
Currently no, the story of the game is at the same point as the original game. Story will be developed further in future versions, however it is not currently the priority :).
As I’ve said on the post below, fullness is a calculation resulting on the number of eggs, incubation progress and size of eggs, determined by each critter. It only serves to indicate how full Leah is, which is reflected on the belly size. Nothing happens at 100% it is only an indicative number, Progress is the important stat.
It fills up as eggs grow, but when Progress reaches 100%, eggs stop growing, so Fullness stops as well.
Parasite Worms don’t grow above 28% on version 1.30. If you want to see bigger fullness, you have to cure all parasites and incubate other critters.