Within Teamwork.com, you can break your teams down further by creating subteams.

Note: Subteams are available on per-user Premium/Grow subscriptions and above.

When you are creating a team, you can make it a subteam by assigning a parent team to it in the Advanced tab.

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Alternatively, click the three dots to the right of a team in your teams list and select Add subteam from the dropdown menu.

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When a user is added as a member of a subteam, they will automatically be added as a member of the parent team and any other subteams above it in the overall team hierarchy.

For more information, see: Adding a Team