You can run a batch campaign that is looking for those who are exhausted in the higher priority stream and the flow will be to move them to the lower priority stream. The leads will still have a normal cadence, so all you will need to do is move them to a new stream and they will begin to receive any new content in the lower priority stream.
The new stream will need to be chosen manually. Unless you build a new custom field that populates with the name of the previous stream and use choice conditions to then add to the stream that the lead was previously in.
Change engagement program stream
Choice 1: If Previous Stream is "Stream 1"
add to Stream 1
Choice 2: If Previous Stream is "Stream 2"
add to Stream 2
Sorry I think I was unclear - I don't want to move them to any old stream, I want them to move to the stream that they were previously in to finish it. Like this:
Stream 1 - Getting that good content... Hold up! I've got some better stuff for you. Pause.
Stream 2 - Here's some way better stuff my man. No? You don't like that? Exhausted.
Stream 1 - Here's the rest of that classic good stuff. Exhausted.
Right. So create a new custom field for the "Previous Stream". Use the trigger of "engagement program stream changes" with the constraint of "Previous Stream" and the flow will be to change the data value of the custom field to the name of the previous stream.
Ah, your updated post nails it. Thank you!