You definitely can. What you’re looking for here is the Who can message this group? setting.
Navigate to the group page for the group you wish user to be able to message, admins, moderators, or staff (moderators and admins). Then switch to the “manage” tab. From there, you can enable the ability for users to message the group. Messages will only be visible to the user who starts the message and the group. Additional users can be added the message if wanted as well, supporting a message between user a, user b, and staff, for example.
