I generally agree with what @katja_keesom is saying, but I would be careful with the following quirk of engagement streams:
The streams can be built with smart campaigns (the bulbs) or with email assets (the email icons) and it matters.
If you want people to go back to the spot on the stream where they were, you could leverage pausing the cadence in the old stream and add them to the new one, then pausing the cadence in the new one and resuming the cadence in the old one.
But keep in mind that if you just add a person to a stream (instead of resuming their cadence), if the stream is built with emails, during each cast, Marketo will check if the person has received any of the emails on the stream before, then pick the next one they haven't received.
If it's built with smart campaigns instead, Marketo will check for membership but what is going to happen is: if the person is a member of the first campaign on the stream, it will do nothing that cast. Next cast, same thing, if the person is a member, they get nothing.
So keep in mind that depending on how you built it, when moving people to and from, there is a scenario where people may not receive anything for some casts if you just add them instead of resuming.
Hope I made my idea clear. And if Marketo has removed this limitation by now and I'm not aware, please someone let me know!