Generally Data Level security will take a customization of the existing module or a new custom module.
What I could see you doing instead is this:
for the announcements module:
Add a module Announcements and make it visible to Role 1, 2 and 3
Add a 2ned Annoucements module and make it visible to only Roles 1 and 2.
Make a third one only visible to role 1.
Somone in Role 3 would only see the announcements in the first module, while someone in ROle 1 would see all of them
However, if this is by user (instead of by role, or if you had 1000 roles) this may not be particularly practical.