The short answer is: you cannot. At least not for generic scalar potentials.

The simplest example I know comes from duplicating the number of Higgs doublets and extending it to the 2HDM. Here, vevs can break charge or CP spontaneously depending on the parameters:

https://arxiv.org/abs/hep-ph/0507224

For the 2HDM potential, the whole story is pretty much known and we know how to ensure neutral vacuum. But the vacuum structure is already much richer than in the SM.

Generically, if the scalar potential contains few multiplets (e.g., one), it may not be difficult to check that neutral vacuum is indeed what you get for some parameters. But with increasing number of fields, the problem quickly becomes very complex.

There are different problems with different degrees of difficulty, though.

1. Ensuring the vev is local minimum. This is what is usually done. Test that the vev is stationary and then checking the masses-squared (2nd derivative) are positive definite. The latter ensures that it is a local minimum. Also, some of these problems are often bypassed by demanding what type of vev you want an adjusting the potential parameters to achieve that.

2. Checking that the vev is the global minimum for some parameters. This is a much more difficult problem as one needs to check if there are more stationary points for the same set of parameters.

3. Map all the possible symmetry breaking patterns (construct the phase diagram). This the next step where you know everything you need.