In a recent posting I looked at Parfit's account of the formula of humanity in his original 2002 lectures, the "germinal core", so to speak, of On What Matters. What is apparent from the consideration given in 2002 is that the discussion of "rational consent" is separated out from the reference to not treating persons "merely as a means" in Kant's formula. This separation of the reference to "rational consent" from the discussion of what is involved in not treating someone "merely as a means" in 2002 continues in Parfit's subsequent drafts of what eventually became On What Matters.
The second version of Parfit's work is the manuscript that goes under the name Climbing the Mountain which is available courtesy of Pea Soup. In Chapter 4 of this work we find a correlate of what was the first lecture of 2002 and it opens in a very similar way discussing, as it does, the Formula of Humanity and drawing out the same problems with the readings of Korsgaard and O'Neill that were already stated in 2002. Similarly, examples are appealed to that are meant to show problems with desire-based "subjective" views of reasons. Finally, the rape example is again used to bring out problems with thinking of consent only in terms of "possibility" and to show the need for some sense of "rational" consent.
New material begins to be discussed in Climbing the Mountain when Parfit turns to "deontic beliefs" concerning other reasons than consent for finding something to be wrong. Considering independent reasons for finding something to be wrong Parfit now builds into the "consent principle" a sense that we cannot consent to something that we have other reasons to find wrong. However, after making this point, Parfit's discussion takes an unexpected turn as the kinds of examples he goes on to consider lead in the direction of considerations touching on beneficence. This leads, in a now fairly traditional style to indications of why I should sacrifice things that would satisfy myself in order to morally help others.
In support of what may appear here to be consequentialist question-begging, however, Parfit can cite Kant's remarks concerning how the ability to be beneficent depends itself on situations that are unjust and on Kant's claim that it is possible to "participate in the general injustice even if one does no injustice". However, in the passage from the Doctrine of Virtue where the most extensive account of beneficence is given Kant also allows that practicing this virtue at one's own expense is something that is not permissible since it would merely create a new case of someone needing beneficence, something that Parfit concedes and uses to temper his account of the duties here involved. In conceding this Parfit indicates that acts that would be morally permissible are not necessarily morally required.
What Parfit does not sufficiently explain here is how he has been led from "rational consent" to these questions concerning beneficence. The bridge appears to be that others could and would consent to my doing acts that would decisively aid them even if this required me to engage in considerable sacrifice. So the link seems to be one in which the consent of others appears as a kind of demand upon me by virtue of what it makes permissible for me. It is not so obvious however that a concern of this sort was at the heart of the false promising case that led Parfit, along with others, to assimilate the Formula of Humanity to a principle of rational consent.
Further, since some acts are wrong despite our being able to consent to them, it follows that the Formula of Humanity has not been well captured in being assimilated to the notion of "rational consent". This concludes the additional material of Climbing the Mountain on this topic.