I already have NHIS but I have heard that many people also get private health insurance in Korea?

NHIS covers the basics, but many people add indemnity insurance (실손보험) to cover the out-of-pocket portion, plus riders for cancer or critical illness. Foreigners with an ARC and a stable visa can buy from insurers like Samsung, Hyundai, or DB, with premiums depending on your age and health. It's worth it if you want much smaller bills for serious treatment, but read the exclusions carefully, especially for pre-existing conditions.