New wort blended with fermented beer

I know that people do with sour beers (can't think of the name right now), I am asking for any tips or ideas on adding new wort to beer that has already been fermented and is still in primary. The plan is to try to get as consistent of a product as possible, as well as utilizing the active yeast cake as much as possible. To start I would probably be using a 15 gallon sanke and adding 6-8 gallons to it over two brew sessions with around 3 weeks in between. Then let the second batch ferment out and keg it all.

But I've also been throwing around the idea of getting a 55 gallon drum or barrel and using that to constantly add and pull off beer. My biggest concern is leaving the yeast cake in the barrel, won't you get autolysis after a while? Is this where everyone tells me to get a conical so I can drop the trub?

Solera is what I was thinking of.

Why not just ferment, rack off the beer and reuse the yeast cake? I wouldn't worry so much about autolysis as much as oxidation. I've brewed on two consecutive days to fill a large fermentor, but I don't know that fermenting out and then adding more wort has any positive effects.

I have an 11gal solera-style barrel for sour beer, have pulled two 3gal batches off it. GOod stuff so far, but this is sour beer not regular.

Thanks for the thoughts. I was actually thinking it would save me one racking, hence reduce oxidation/infection chances (plus I'm lazy) but I guess I would need to add oxygen to the second batch somehow huh? Hence oxidizing the first batch. Hmm...