I have no idea what "without having to unplug the fully charged battery" means... but I bought one of these and love it...

https://www.amazon.com/gp/aw/d/B08J7M1MPL?psc=1&ref=ppx_pop_mob_b_asin_title

It can charge 4 batteries and a USB device (ie. controller) at the same time. Bonus is that it has a car charger plug too.