Can a Croatian citizen extend their visa in Thailand or needs to apply for a new one at an embassy?

A Croatian citizen cannot obtain a visa on arrival and must go through an embassy for visa approval. As their current visa is expiring, they inquired about options for extending their stay. It is possible to obtain a 30-day tourist visa extension as long as one has not already extended their visa. Alternatively, they can leave the country and apply for a new tourist visa at a Thai embassy in another country.