Would it be possible to add additional option(s) when responding to approval requests within Requests and Changes so that they appear in the list of options next to "Choose" in the below screenshot?

An example situation where an additional approval response may be helpful is for instances where approval is sent to the incorrect user. You could implement a third option to "forward" the approval, assuming the recipient knew who the approver should be. You could add a name for the type of approval response, ie 'Forward', and then customise what that approval response does (in this case, allow the approver to select a new approver to receive the approval notification).

As it currently stands, the request often has to be duplicated for approval to be resent to the correct user. Alternatively, an additional approval stage has to be added and the original unintended recipient has to approve to send the next approval stage to the correct user.