How do you calculate time dilation if there's two gravitational pulls acting at once?

I was wondering how you'd calculate time dilation if there's two masses acting on you at once. For example lets say I wanted to calculate the time dilation between Earth and PlanetB (I just made that up idk) but PlanetB was really close to a black hole who's gravity was acting on it. How would I combine the gravity of the black hole and the gravity of PlanetB itself to find the time dilation. (Ignoring time dilation from velocity)

It is, as it turns out, very difficult to do this.

The reason is because the key equations of general relativity - the Einstein field equations - are highly nonlinear. This means that if I have two solutions to it (e.g. the solution for PlanetB and the solution for the related black hole), adding them together does not produce another solution. In the weak-field case, as for anything less-intense than a neutron star or such, you can approximate the fields in a linearized way so that you can get a good estimate of what things should be; for a black hole, though, that's not possible, because the linearized approximation fails in such cases.

For two planets, gravity is roughly linear, so time dilation would just be

$$\sqrt{1-\frac{2G}{c^2}\left(\frac{M_1}{r_1}+\frac{M_2}{r_2}\right)}$$

for the mass of and distance to Planet $i$ being $M_i$ and $r_i$, respectively. If you're talking about a black hole and a planet orbiting close enough that that matters, the gravitational time dilation will be very different; determining it will require identifying a two-body vacuum solution of such a form, which to my knowledge has not yet been accomplished.