Can phase diagrams be obtained by Helmholtz energy minimization?

I know that in calculating phases of materials it is standard to choose a pressure $p$ and temperature $T$ of interest and then, keeping these two quantities fixed, find the mixture of phases that minimizes the Gibbs free energy. This then has to be the themodyanimcally stable mix of phases.

But naively, you could make a similar arguement with Helmholtz free energy. You could choose a volume $V$ and temperature $T$ of interest and keep these fixed, and find the mixture of phases that minimizes the Helmholtz free energy. At constant V and T, I would think that this should be the most thermodynamically stable.

My question is: is it ever possible to find the phase diagram this way? If yes, would the predicted phases be different than the standard Gibbs minimization. If you can never use Helmhotz energy to find phases as described, why is this not possible?