I want to manage suppression lists for my team...
Creating suppression lists, including duplicate prevention across your team or within your account is described in detail in this post.
I want to manage different suppression lists for my clients...
In the case where you may be managing multiple accounts (ie - you run an agency or consultancy), you may need to create Teams within Teams so you can have suppression lists and/or duplicate rules applied within a specific team and not applied across all teams/users.
To set this up, make sure you invite the Team Admin (ie - your client's main point of contact) and their coworkers to join your Team so you can manage billing. Once they've accepted the invite and granted you Account + Campaign permissions, you'll be able to access their account.
Let's look at an example scenario where you have 5 client accounts each with 4 team members (ie - 20 accounts you manage) who've successfully joined your Main Team:
If you go to your Suppression List and apply rules (like prevent team duplicates) all 20 of your clients will be subject to the rule. This can create a problem in the scenario where 2 or more different clients need to contact the same person. If you have Team Duplicate prevention turned 'ON' then once 'John from Client 1' emails 'prospect Ryan O'Donnell', Susan from Client 2 (who also has Ryan in her campaign) won't be able to email Ryan.
To prevent this from happening, if any of your 5 clients have specific requirements for creating suppression lists or if they want to prevent duplicates across their coworkers, you'll need to Create a new Team from within your client's accounts (ideally the client admin/main point of contact).
Provide them with these instructions or 'Switch Accounts' into their account to set this up.
From the client's account, go to their Team Section. Every user account has 1 default team that they are the owner of even if they are part of the Team you (the agency owner) already invited them to.
Click Manage/Invite for the Team that you're going to create.
You can invite your coworkers one by one or you can use the 'Team invite link' to invite your coworkers by sending them a direct link to confirm and grant permissions.
From the client's account that just sent the invite, go to the Contacts Section and click Manage Suppression to create specific rules for this Team.