First, Parfit notes, one might violate the spirit of this principle by treating someone as a minimally significant end. He thus proposes:
The Second Mere Means Principle: It is wrong to treat anyone merely as a means, or to come close to doing that.
The next problem is that one might perform the right act for the wrong reason. If an egoist saves someone's life merely as a means to receiving rewards, his act lacks moral worth -- he isn't virtuous or genuinely praiseworthy -- but he does not thereby act wrongly. (Cf. Scanlon on the irrelevance of intention to permissibility.)
Parfit takes this to motivate:
The Third Mere Means Principle: It is wrong to treat anyone merely as a means, or to come close to doing that, if our act will also be likely to harm this person.
I think the formulation of this emendation is ad hoc and fails to get at the heart of the problem. To see this, note that it faces similar counterexamples to the previous principle. Simply imagine a case where it would be right to act in a way that is likely to harm a person (perhaps it's a small harm, which the subject has consented to, for the sake of preventing a much greater harm to the subject's child), and imagine that the egoist performs this right act for the wrong reason -- treating the subject merely as a means, and thereby violating the letter of this third principle. The principle then implies that the act was wrong, contrary to Parfit's intentions.
A better alternative, it seems to me, would be something like the following: It is wrong to act in a way that is incompatible with full appreciation of a person's rational nature and status as an end in themselves. We might call this the Full Appreciation Principle.
The "full appreciation" clause plays the same role as Parfit's disallowing "coming close" to treating anyone merely as a means. And framing the requirement in terms of what's (in)compatible with full appreciation does a better job than Parfit's proposal for accommodating the full range of cases where one might perform a right act for the wrong reason.
One possible downside is that it is less clear precisely what demands the Full Appreciation Principle places on us. We can easily enough grasp what it means, in ordinary language, to treat someone merely as a means. As Parfit points out, you clearly don't treat someone merely as a means (or even come close) if you let yourself die rather than crush their second toe (even while you crush their first toe as a means to saving another person). He further argues that we won't violate any of the Mere Means principles if we constrain ourselves to only treat people in ways to which they could rationally consent. And one always could rationally consent to enduring some harm for the sake of another's greater benefit (we may be permitted to favour our own interests, but we surely aren't required to do so!). So the Mere Means principles don't really rule out anything controversial at all -- certainly not the standard sorts of utilitarian sacrifice that Kantians typically want to rule out.
So maybe that's actually an advantage of the Full Appreciation Principle: since it isn't clear what it amounts to, it remains open to Kantians to put their distinctive spin on what "full appreciation of a person's rational nature" requires, yielding a principle that actually rules out utilitarian sacrifice the way they want it to. Though, admittedly, it means that appeal to the intuitive flavour of this principle can't do any work for them (since utilitarians and others can just as easily put their own spin on it); the real work is being done by their prior account (whatever it may be) of why "full appreciation of a person's rational nature" rules out utilitarian sacrifice.