Skips,
Yes, absolutely.
Modules have individual view / edit settings. So, let's say you want someone to edit the Announcements module, but like you said, not add/edit/delete other modules on the same page.
You need to:
1. Under Security Roles [Admin > Security Roles] for your portal, "Create New Role" that your annoucements module editor will take. You will probably need a new role, b/c the existing Admin role is too broad for this operation.
2. Update the User's Roles in user administration on your portal to include the new role created above, so that user is added to that security group.
3. Edit the module that you desire this person or user group to have edit privileges on. That is, A) Add the module to the page, B) Hover over the little triangle on that module, Select Settings. When in the settings view, Under Module Settings > Basic Settings, check the box in the Edit Module column next to the security role you created in step 1 above. This way, the user accounts that have the, let's say, Edit Announcements role, will be able to add/update/delete announcements only within that particular module, leaving you with full Admin rights on the page itself.
Feel free to reply with more questions.
Regards,
Vollerworld