It is! There is a feature to help creating new organization that is not currently enabled by default so the first thing you'll have to do is send a note to email@example.com asking them to enable new account creation for your organization.
Once your organization has been enabled you'll be able to access the account creation page to define new orgs: https://app.datadoghq.com/account/new_org
After creating your organizations, you'll be able to switch between them by hovering over your avatar in the lower left hand corner.
Once the menu appears, you can transition to the other Datadog accounts you're associated to:
Once the new account has been setup, you can invite people to your new org from the Team page the same as you would your regular account.