Ted here from Shopify, thanks for posting your query!
This is a great question! It is quite rare that a gateway can accept two bank accounts but it might be possible.
If your client is using Shopify Payments then I can confirm it is not possible to use two separate bank accounts to accept payment. Only one bank account can be used. Here's a list of bank account requirements from Shopify Payments if you would like to take a look. In regards to other third party gateways, I'd recommend contacting your clients chosen gateways customer service for more information.
If there is anything else I can help you with, please let me know, I'm happy to help!