I know for a fact that axis bank employees are eligible for 4 cards at a time. Once i had also enquired in a branch. They said it is not possible to issue 4 cards to one customer.
But i think if you are desperate enough, u can try something like this -
Try applying online through a different mobile number. Its not confirmed but i think it is a loophole.
If that doesnt work, you can always apply through a family member. That surely works.