My common port BMS only have P- and B- . No C-. Isn't that the point of a common port? They charge thru the discharge connector. I still put a charge connector in parallel with the discharge port. MAybe I don't follow your question,
I recently had to bypass a new BMS that I had installed on a used Uber ebike battery I bought for 40 bucks. The cells were down around 2.90V and the BMS wouldn't allow a charge. I unplugged the balance cable and put a charger directly across the cells until the cells got to about 3.3V. Then I reconnected the balance cable, and now the BMS allows a charge. Shouldn't have to do this again.