You can apply for more rights shares than the RE’s you have but allotment will be guaranteed to the extent of RE’s you hold, for extra quantity, allotment will be done on lottery basis, if you don’t get allotment for remaining shares, amount will be returned back to you.
You can apply through Netbanking ASBA or the RTA’s portal.
You’ll have to make seperate applications from both your Demat accounts.
Eg. let’s assume you have 100 REs in your Zerodha account and 50 REs in your other account. Later, you purchased 20 REs in your Zerodha account.
Accordingly, you’ll be able to apply for 120 rights with your Zerodha demat and 50 rights with your other demat. This won’t be considered multiple applications, since the RTA is performing the check based on demat account and folio. If you apply for 170 shares with your Zerodha demat, the RTA may only allot 120 shares out of entitlement and the rest 50 shares may or may not be allotted during a lottery.