hi brindle,
what you have shown in your schematic is exactly what happens when two or more 'protected' cells are connected in series, and you can purchase small PCBs containing a DW01A and a pair of MOSFETs ready to wire across individual 'unprotected' cells.
where things get complicated is when you are charging 2 or more 'protected' cells in series, and one reaches full capacity before the other(s). there is the possibility of the DW01A of the full cell opening the over-charge MOSFET for that cell, which will then prevent further charging of
any of the other cells in series.
in an ideal world you would therefore have charging connections for each individual cell (so for a string of N cells there would be N+1 connections) and have N floating chargers, one for each cell.
the BMS for multi-cell packs may get around the problem by having shunt transistors across each cell that start bypassing current when a given cell reaches the 'full charge' voltage. but i have never really liked this solution as (a) it wastes power, (b) it may interfere with detecting the current drop-off at end of charge, and (c) most implementations i have seen seem to be rather badly designed.
for one such balancer design, see here:
https://320volt.com/en/simple-balancer-circuit-for-li-ion-batteries/
but note that this circuit will continue to draw current from cells (through R1+R2) after the charging current is removed. really this sort of circuit needs to be isolated from the cell when not charging - and indeed, when equipment is turned off there is no need for
any of the battery protection or management circuitry to be connected.
cheers,
rob :-)