Hi Marissa Dimino,
For my answer, I'll assume you are referring to the Jive Inbox, as opposed to a user's personal email inbox. Although there are not settings within the Admin console to control what types of activity users receive updates for, there are two ways that users can control notifications themselves when they are not wanted.
The first option is that the user can choose to follow that Group or Space's activity in a stream rather than their inbox. To do this, they click the Following button located on the Place's overview page, uncheck the Inbox option, and check the stream where they would like to follow that Place's activity:
In this way, they can still monitor activity that occurs within that Place while avoiding notifications in their Inbox.
The second option is more granular in that it targets the piece of content that is being liked or commented upon directly, rather than the place where that content resides. When viewing any piece of content in the Inbox, users have the option to select Hide New Activity. You'll find this option just above the content when viewing it in the Inbox:
This will allow the user to discontinue receiving notifications for any piece of content that is creating to may notifications.
We just had a similar question come up in our community. Although I recognize this answer is the right one for Jive's current state of development, it's not particularly satisfying from these users' perspectives. They want to know when new content is added to a place they're following, or by a person they're following, but they consider the social and action signals (Like, Helpful, etc.) to be unnecessary noise. Unfollowing an entire place to avoid these notices is overkill that results in missing relevant content. Muting a single item at a time is an unnecessary burden, probably wouldn't be done very often, and would result in missing an important comment just to avoid the Like notifications. It's using a sledgehammer to get a fly off your window.
To be clear, this is not true of everyone. Some of us are fine being notified of Likes as well as new content. But it would be nice for the others to have a way to turn off specific types of notifications across the board, just for their accounts.
You may want to create an improvement idea around a more granular way to control notifications in our Ideas for Jive Space, where improvement Ideas are voted on by members of the community and reviewed for inclusion in future versions of Jive.