Ideal gas law vs van der Waals equation of gas

$$ ( P + frac{n^2 a}{V^2})(V-nb) =nRT$$

is the van der Waals equation of state

and,

$$ PV=nRT$$

is the ideal gas law.

Similar to how I asked in this stack , prof. Moungi Bawendi says that as we drop pressure to zero by some mechanism, the product of pressure and molar volume converges to some constant based on the temperature and uses this to define the ideal gas law.

Now, could we start from van der Waals equation and work back to a more accurate f(T) which converges more broadly than it does for an ideal gas? if so, how do we do it?