Hi Rahul,

Yes it is completely legal. You can complete both your degree and diploma at the same time.

I am currently doing my B.Sc. and diploma together as well

It is allowed as long as the degree providing college or university allows you to go for another diploma. If the administration is okay with it then you won't find any problems.

I would suggest you to go and get your doubts clear about this by talking to someone in the administration.

I hope it helped.

All the best!