Visa/Mastercard requires all cardholders, cardholders' banks, merchants, and merchants' processors to follow the comprehensive set of rules for disputed transactions. That way the dispute process tends to be uniform across different banks and across different merchant/payment processors.

The network sets the rules, while the banks implement those rules on behalf of the cardholder and the processor implements those rules on behalf of the merchant.

So replacing the network will require a comprehensive replacement for the network's dispute resolution rules (assigning who is responsible for paying when certain things happens) and procedures (how a cardholder can initiate a dispute and how that gets resolved).