While you can apply, only one will go through, likely the upgrade as it is processed with almost zero human interaction and it is guaranteed to be done in a few minutes (through OTP for confirmation of upgrade). The old card will be deactivated only after 45 days, though.
Our fellow member @binno tried something like this, last month and got rejected upon the consecutive application. Incidentally, he too applied for Airtel at first (and got approved), and then tried for another card.
I would recommend the following… Go ahead and apply for Airtel card. You will know the result in about 15 days. If rejected, you can upgrade the existing card. After 90 days, both Airtel and Axis will allow you to apply for Airtel Axis CC again.