before opening the account, please clearly ask bank branch manager about the cards & facility for transaction.
I strongly believe that cards issued to account(s) opened using single CNIC from 1 BANK with accounts at different branches are consolidated and transactions limits does not change.
be very specific and seek clarification, or the purpose of your whole excercise will not be served.
my 30 year old citibank VISA card was merged with the HBL card after HBL took over Citibank card operations in Pakistan. The HBL card upgraded to black, but .. the per day transaction limit over internet did not changed.