Are FHIR extensions supported?

We do support extensions on all FHIR resources. You can test out the conformance of any resource on each resource page, for instance the Patient dstu2 resource or via API.

For example see this patient resource with the extension which you can paste into the validator.

{"id": "1", "name": [{"given":["Scott"]}], "extension":[{"valueString":"abc", "url":""}]}