I guess have an 'out of band' observable? Each observer that needs to communicate instruction back to the original observable can drop messages into an OoB observable, the original observable can subscribe to the OoB observable and then react to those messages as it sees fit.

Or do you think it should be an inherent feature of the stream itself? Isn't the point of IObservable to be the dual of IEnumerable, so calling Select on IEnumerable is a projection from A -> B, calling Select on IObservable is also a projection from A -> B, I think having an additional effect breaks that duality. So an Observable that has a side-channel or out-of-band stream wouldn't be an Observable, it'd be another category (which is why I suggested Pipes).

I totally understand why you'd want something like that, I'm just not sure it's fair to suggest Rx has design mistakes because of this though.