I have used CLL with both monolingual and multilingual classes and found that it works well with both. With the multilingual low-level classes I, as the teacher-counsellor, reformulated their English in the same way you might do with higher levels. However, the first few attempts at CLL work better with a monolingual class as the instructions can be given in L1. It's important that the learners understand their and your new roles in the language learning process.