Hello.
Technically there will be no problem, your CBSE marksheet will still be valid if you have another one of NIOS now  it's easy to apply for both board simultaneously CBSE and NIOS but if you are going to use both simultaneously then I would suggest you to don't do this because this is an illegal process even if you are going to take admission on the basis of your either of the marksheet then it will work but it depends upon your marks in the  marksheet if you are passed then you can use else fail marksheet will definitely doesn't allow to take admission in any of the college or for using other purpose.
Best of luck.