You can likely pay a local agent to do a 30 day tourist extension, 1 time, you may be able to avoid an actual trip in.
For anything past that 30 days.
In all cases, without a local diagnosis from a hospital/doctor and a document explaining the reason you cannot fly, you will not get an emergency medical extension.
You will need a local agent and a fistful of money, to find a possible workaround.