In this case, you need to build a plugin that will include different payment methods required by your client. I'd recommend installing multiple plugins and have a step where a customer picks up payment methods. You can also customize the UI for this step to use drop-down, etc. You will have to build similar screen for your new plugins anyway.
You can also try to customize the theme and have both screens on one page together, but it will be more work than just a new UI for picking up a payment method.