Shkadov thruster:
> After a period of one million years this would yield an imparted speed of 20 m/s, with a displacement from the original position of 0.03 light-years. After one billion years, the speed would be 20 km/s and the displacement 34,000 light-years, a little over a third of the estimated width of the Milky Way galaxy.
Caplan thruster:
> Caplan estimates that the Bussard engine would use 10^12 kg of solar material per second to produce a maximum acceleration of 10^−9 m/s2, yielding a velocity of 200 km/s after 5 million years.
Svoronos Star Tug:
> The Svoronos Star Tug can, in principle (assuming perfect efficiency), accelerate the Sun to ~27% the speed of light (after burning enough of the Sun's mass to transition it to a brown dwarf).
If you're K2 just take the star and solar system with you. Stellar engines can be used to move stars. https://en.wikipedia.org/wiki/Stellar_engine