Yes, this is possible in Shopify Plus. You will need the Script Editor of Shopify for this.
Please refer to this page for more information: https://help.shopify.com/en/manual/apps/apps-by-shopify/script-editor
I believe there are some examples in this app. Note that some knowledge of Ruby is required, so it is not an easy thing.
You are able to change the order of the Payment methods and it is also possible to hide a payment method in some circumstances. For instance you only want to show payment methods applicable for the shipping country.