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how to finish Jessica's story  "i should keep investigating, and learn more about the Organisation"

(+1)

I answered before but I don't think it's that easy to look for answers in the older posts. 

REPOST:

You need to progress with the organisation branch of the main story.

I'd say follow the leads, but you may not have the leads, so check this sequence if you missed a step.

Go to the manor's garden and check the note.
Take a train to visit Gramps.
Ask him questions.
Do the 4 levels of training.
Ask again.
Go to the lake and search 3 times for the pigeon.
Talk to Gramps again and you should unlock the main story leads.
Ask him about each lead and then follow them.

The Organisation one is for Jessica.