Yes, Act! 365 will give you the ability to add the same contact to multiple Groups.
Start in the Contacts section
- Look up desired contact in Search field
- Click the contact's name
- Click the Group tab
- In the Add a Group...field you can click the drop down arrow to see all groups created and click the one you want to add the contact to
Note: If you want to create a new group for the contact, type the new Group name in the Add a Group... field and click enter from your device key board