CET-4 is enough, and there are some graduate students among my classmates who have not passed CET-4. There is no requirement for English proficiency in the entrance of Communication University, as long as you pass the national single-subject English score line, because English for postgraduate entrance examination and CET-4 and CET-6 are not the same type of examination at all. After CET-6, people who scored low in postgraduate entrance examination can also be seen everywhere, and it is easier to retest oral English and listening. Generally speaking, the re-examination ratio is 1: 1.2, which will eliminate a certain number of people.
I hope you can succeed.