That depends on how you are retrieving the initial item. If you are using liststreamkeyitems with appropriate start and count parameters, you can easily adjust those parameters to get the previous or next item.
If you're retrieving in some other way, I'm afraid there's no easy answer. If your stream has few different keys, you could just check for other items with the same key in that same block using liststreamblockitems with the initial item's blockhash. You can also page through blocks using the previousblockhash and nextblockhash fields of the getblock API with that same block hash. But this won't be efficient if there are many different keys in your stream.