Split payment-method section in two parts?

In my payment-method section, the user first chooses the form of payment, and then presses the ‘Pay’ button. Before this section, there’s the checkout form, where the user enters their personal details.

I’d like the order of the above to be:
1. Select form of payment.
2. Enter user details.
3. Press ‘Pay’.

Does this plugin allow me to do this?