Good question.
My thoughts are that I'll add a small starter, probably 1 L in my case, since my London ESB yeast is liquid yeast (and I want a meaningful starter). I've heard 1 pint and a packet of dry yeast is sufficient for this method. In my case, I'm not worried about getting too much attenuation from the London ESB yeast. It gets pretty lazy as the sugars dry up. Worst case scenario, I could cold crash it near freezing in one of my chest freezers for a few days before I keg it and force carb it.
I was thinking I would cool the beer back down to about 68 degrees before repitching. I don't want the fresh yeast to ferment too hot. I am a little concerned about oxidizing the beer with the new starter, though I haven't found anyone citing this as a problem or concern. Presumably the new yeast will use up the oxygen before it drops out of suspension.
It seems worth a shot. As I searched through the forums, I didn't find a downside to this...other than simply wasting money on the new starter (if it doesn't work).
Generally speaking, I don't think you have to worry about getting too much attenuation from pitching an active starter of the same yeast you started with into a stuck fermentation. I haven't heard any horror stories. I have heard people reporting that they didn't get any further drop in gravity points at all from this method. So, it seems a lot like worrying about overdoing it at the gym because you don't want to be too muscular.
Hopefully, I will see some progress.


