Overriding Coupon Code REST API

I would like to send an extra Header argument in the PUT V1/carts/:cartId/coupons/:couponId that is utilized by the REST API (that handles that PUT request). To do this, I would like to override that REST API, appending my own code to parse the custom header. However, everything I have found on the internet pertaining to overriding existing magento 2 REST API calls/methods have not been particularly useful to me. I know that the code is in vendor/module-quote folder, but I don’t know how to override this specific PUT coupons API call. Is it possible to to so? I just want to be able to send it a custom parameter/header and be able to make the proper adjustments so that the corresponding REST API actually does something (that I want it to do) with the custom parameter/header.