Hi.
3.5~4.2 down to 3.3V, max 400mA.It would help if you were to state the acceptable range of output voltages and the temperature range over which you require that accuracy.
The capacitive load that will exist should also be given to enable stability analysis and help narrow the viable design approaches. For the same reason, if transient loads will not be absorbed by the load capacitance, they should be specified as well.
The circuit is going to exhibit a TC of about
13 mV per degree C, within a few mV. If the output is to power logic requiring a 5% supply, that drift alone would constrain the operating temperature to stay within a 12 degree C band. But the initial tolerance is going to be poorer than that, due partly to variation in BJT beta and partly to the varying threshold voltage of the MOSFET.The MOSFET is backwards.
adding a lot of parts.
It would also help if you were to indicate the cost constraints applicable to the solution.
I guess a zener is also a candidate, (although low voltage zeners are very soft references.)
Before designing improvements, it would be smart to nail down the requirements and separate them from the wishes.
You may see a number of circuits offered here as an "improvement". They may not satisfy your actual requirements unless they are stated ahead of the time those circuits are concocted. But if you have stated your requirements, the circuits offered will be scrutinized against them, at least by some diligent participants.
You're most welcome.