So, I'm not sure if you're talking about discussions per se, or Salesforce content that has been streamed into a place in Jive.
In the first case, you could discuss any content privately just by linking the content in a discussion, or sharing it via Jive Anywhere, and setting the permissions on your discussion to be just you and whatever users you want to include. You can either start a private discussion using the Direct Message functionality, or using Create > Discussion from the create menu (if you want the option of later moving it to a place or the whole community, and using the more fully featured discussion functionality--in this case, select Specific People in the publish bar and identify them). In either case, the discussion will be private to only the people you added.
If you're talking about streaming Salesforce content into Jive, and then commenting on it, who can see it or reply to it depends on the permissions of the place where you put it. For groups, the content can be in a private or secret group. Space permissions can identify specific people or users groups, but keep in mind that subspaces inherit the permissions of their parent spaces. If you put the content in a private group or a different space, your Support space users wouldn't see it if they didn't have permissions to the Salesforce location.