Charging a 4000mAh Li ion battery using multiple TP4056 ICs
The TP4056 is LINEAR charger. As such, at 1 A charge current and 6V power input, it will dissipate (6v-3v)*1A ~= 3 W. This is a lot for a small PCB to dissipate, and the chip will be HOT. If you use Schottky diodes, they will drop a bit of voltage difference, but not much. 

If you want to fast charge your 4000 mAh battery (at up to 1C rate) without dealing with much of heat dissipation, you need to use switching-mode chargers, like Texas Instruments BQ24xxx- BQ25xxx series, or similar. 

And if you are designing a solar-powered backup, you will be wasting a lot in linear chips and diodes, and it might need a more sophisticated engineering.