SQL: Filter out entries that appear more than once

I'm new to SQL and hope to find some help here. English is not my native language so if something seems unclear feel free to ask!

Like the topic name implies I want to filter out entries (Strings) from a table that exist more than once.

My code looks like this:

SELECT DISTINCT characterid, firstname, lastname, courseid
FROM Teaches
NATURAL JOIN Character
GROUP BY characterid, firstname, lastname, courseid

And it gives me this:

Table

The task is to filter out everyone who teaches more than 1 course. In this case it would be Snape and Quirrell. I tried it with counting

HAVING count(characterid) > 1

But that didn't work. I would be very happy if someone could help me and maybe explain why that count didn't work. Thank you in advance!

EDIT: If I say "filter" then I mean I want it as a result table. So that in the end I get a table with 2 rows with 1) characterid Severus Snape 2) characterid Quirinus Quirrell

Sorry for being so unclear. Also I only included the courseid in the SELECT statement to see who teaches more than one course more clearly. The final table should only have the three columns "characterid", "firstname" and "lastname"

EDIT2: Here is the structure of the data base. Maybe I'm completely wrong so it could be helpful to you guys: Structure