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 g..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’s keyboard.