Yes, it is definitely possible. But the only condition is that a student cannot give exam simultaneously from both CBSE and NIOS, and the exams have to be in the different sessions.

Like if you have given the CBSE examination in 2018, then you can give NIOS only after 2018, which is 2019 onward. And yes, you'll get two certificates after qualifying both examinations. Hope I have answered your question. All the best!