Starship can carry 1200t of propellant. Starship has three Raptor 2 Vacuum engines, each with about 3.5km/s of delta-V ISS has an orbital velocity of 7.66km/s , escape velocity is 11.2 km/s. ISS weighs 400 tons.
There are unknowns, how much acceleration can the ISS support without falling apart. Since this is a two step process (change the orbital plane and change the orbital altitude) one will have to plan for avoiding other things in similar orbits. Finally, while I suspect a fully fueled Starship could do this with one tank, if you need to refuel between steps it would be more efficient to change the orbital plane, refuel and then change the orbit.
Putting it into an Earth/Sun concentric orbit might be easier.
[1]: Yes, its all wikipedia and such and no I haven't built a Kerbal model and run it, and yes it would be a "stunt" but penciling it out with some fellow space nerds the numbers aren't "ridiculous." But it absolutely does require the ability to fill up the tanks (maybe more than once) while on orbit.