Questions about Li-ion battery charger and battery monitor chips
Since you stated that you want optimal protection for your batteries, I think you'll like this solution.

I came up with a circuit that takes 4 T.I. BQ24070 charge controllers (with integrated charger/battery supply switching) as the only battery ICs. This circuit allows each battery to be independently charged &amp; discharged, with all (functional) batteries working in balanced parallel to power your load (through a Boost converter). From the information you gave, I think you'll like that each cell is balanced &amp; protected (from both overcharging &amp; undercharging), and the device has fail-over capability in case of one or more batteries' failure (can supply full output voltage from 1-4 batteries).



The non-labelled resistor should be sized as appropriate for the NPN transistor whose base it feeds.
The zener diode & 10K resistor will push 0.7V to the NPN transistor's base, pulling the AO3415 MOSFET's gate low, and enabling output from the cell as long as cell voltage remains above 2.7V (undervoltage/overdischarge protection).