As Ponies says in a comment, you cannot mix OLAP functions with aggregate functions.
Perhaps it's easier to get the last completion date for each employee, and join that to a dataset containing the last completion date for each of the three targeted courses.
This is an untested idea that should hopefully put you down the right path:
SELECT employee_number,
course_code,
MAX(course_completion_date) AS max_date,
lcc.LAST_COURSE_COMPLETED
FROM employee_course_completion ecc
LEFT JOIN (
SELECT employee_number,
MAX(course_completion_date) AS LAST_COURSE_COMPLETED
FROM employee_course_completion
WHERE course_code IN ('M910303', 'M91301R', 'M91301P')
) lcc
ON lcc.employee_number = ecc.employee_number
WHERE course_code IN ('M910303', 'M91301R', 'M91301P')
GROUP BY employee_number, course_code, lcc.LAST_COURSE_COMPLETED