How can I extend my stay in Thailand after 180 days on a Korean passport?

Just knowing where your passport is from isn't enough.

What type of entry stamp or visa are you on?

If you're on the 90 day bilateral agreement you don't qualify for an extension and will need to leave and re-enter Thailand to get additional time. But if you've already been in Thailand 180 days you may experience problems trying to return without a long term visa, as it appears you are trying to live in Thailand without a long term visa. You may be questioned at the airport and asked to show multiple things, and could potentially be denied entry.