While it is fairly established that both fast movement and the presence of gravity make time pass slower as compared to a system at rest / free of gravity, does that mean that there is no way for time to pass faster than in vacuum, or does general relativity also have "faster" metrics?
To be more precise, is there any frame into which one could go for a while, and on returning to vacuum less time would have passed there?
You need to be a little careful with your definition of vacuum. For instance inside a spherical shell of matter spacetime is flat, however time still runs more slowly than it does outside the shell. I'm assuming you have no such trickery in mind, and by vacuum you mean the usual concept of far (effectively infintely far) from any matter.
To a good approximation a time interval measured at some other point in the universe is related to the time interval measured by you by:
$$ \Delta t_0 = \Delta t \left( 1 + \frac{2 \Phi}{c^2}\right)^{-1/2} $$
where $t_0$ is your time, $t$ is the time at the other point and $\Phi$ is the Newtonian gravitational potential at that point (relative to you). So for example, relative to infinity at some distance $r$ from the Earth the gravitational potential is:
$$ \Phi = -\frac{GM}{r} $$
and therefore:
$$ \Delta t_0 = \Delta t \left( 1 - \frac{2 GM}{c^2r}\right)^{-1/2} $$
and time runs more slowly as you nearer to the Earth. Relative to the vacuum in the sense you mean it gravitational potentials are (as far as we know) always negative so time always runs slow compared to flat spacetime.
I guess the question is whether there are any special cases e.g. if exotic matter exists or if spacetime has some non-trivial topology. However I know of none.
