Question: If my account was already KYC compliant, can the bank still ask for a full new KYC just because I want another account?
Answer: Usually no, if the bank can rely on existing compliant KYC records

Supporting evidence:
title: rbi.org.in/Notification.aspx
quote: Further, if an existing KYC compliant customer of a bank desires to open another account in the same bank, there should be no need for submission of fresh proof of identity and/or address
context: ccount from one branch of the bank to another branch of the same bank. Banks are advised that KYC verification once done by one branch of the bank should be valid for transfer of the account within the bank if full KYC verification has been done for the concerned account and is not due for periodic updation. The customers should be allowed to transfer their accounts from one branch to another branch without restrictions, without insisting on fresh proof of address and/or identity andon the basis of a self-declaration from the account holder about his/her current address. Further, if an existing KYC compliant customer of a bank desires to open another account in the same bank, there should be no need for submission of fresh proof of identity and/or address. (xii) Where a customer categorised as low risk expresses inability to complete the documentation requirements on account of any reason that the bank considers to be genuine, and where it is essential not to interrupt the normal conduct of business, the bank may complete the verification of identity within a period of six months from the date of establishment of the relationship. (xiii) For the purpose of verifying the identity of customers at the time of commencement of an account-based relationship, banks/FIs may rely on a third party subject to the conditions that- the bank/FI immediately obtains necessary information of such client due diligence carried

out by the third party; the bank/FI takes adequate steps to satisfy itself that copies of identification data and other relevant documentation relating to the client due diligence requirements will be made available from the third party upon request without delay; the bank/FI is satisfied that such third party is regulated, supervised or monitored for, and has measures in place for compliance with client due diligence and record-keeping requirements in line with the requirements and obligations under the PML Act; the third party is not based in a country or jurisdiction assessed as high risk and the bank/FI is ultimately responsible for client due diligence and undertaking enhanced due diligence measures, as applicable. (xiv) Accounts of non-face-to-face customers With the introduction of phone and electronic banking, increasingly accounts are being opened by banks for customers without the need for the customer to visit the bank branch. In the case of non-face-to-face customers, apart from applying the usual customer identification procedures, there