Theoretically
In general relativity possible paths follow so called time like trajectories. Every point in space-time that you can reach over a time like trajectory is considered part of your universe. The points inside your future light cone is where you can go to.
A parallel universe is not very well defined but it must be something that is not time like connected to you.
Practically we only fly low
In practice it will not be possible during your lifetime.
Often people think astronauts go into space a lot further then they actually do. Objectively going to space is more bragging then reality, they fly low over the surface of the planet
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