I've been pondering on a hybrid setup like in the picture.
The idea is that instead of buying 4 small LiFePO cell to make a car battery, you buy one big one, put it in series with caps and let a voltage booster keep the total voltage constant, and high enough to decrease alternator load.
The caps are meant to be big enough to provide peak amps during cranking so the boost converter can be smaller and cheaper.
When the car is parked you can bring the single cell with you and recharge it in a nice warm place. (Just a LiFePO likes it)
By using just a single cell you can buy/carry a much bigger one that can easily handle the cranking amps, that way it will last longer and the voltage it provides let's you skip one cap in the system. And you save money on a BMS.
The diode at the bottom of the picture isn't meant to let you crank the engine without the battery, it's just there to keep your clock and ECU-memory happy.