Stephen Vaisey, a sociologist at UC Berkeley, suggests that authenticity and being true to yourself is an aspect of modern morality that cannot be easily linked to any of the 5 foundations. He draws on Charles Taylor's work to suggest an "ethic of authenticity" that makes the following actions bad:
* a person marrying for money
* a person marrying someone they respect and like (but don't LOVE) because they want to have children
* an independent documentary filmmaker taking a job making commercials for Wal-Mart

He adds: "If I had to tell some kind of cultural story here, I'd look to the Protestant Reformation (and further back
to one of its inspirations -- St. Augustine), which encouraged people to find God by looking inward rather than outward to external authority and interpretations. It's pretty easy to imagine the transition from looking inward to find God's will for you to looking inward to find "your true nature." This would be one cultural mechanism for explaining the colonization of one's own internal life with the emotional overlay of the ethic of purity."

Michael Wizer (Cincinnati, OH) proposes a moral foundation of FUNCTIONAL (PROBLEM SOLVING) VERSUS DYSFUNCTIONAL

This is related to our very long evolution as creatures who solve problems to enhance survival.  In humans this foundation underlies all other moral judgments regarding the feasibility, efficiency, or workability of behavior.  It is implicit in the judgments that says another person’s or group’s behavior is “wrong minded” or “ignorant.”

Because the judgment of function and the creation of solutions to problems is ubiquitous, it is at times difficult to see it running underneath and through the other moral judgments.  For example, when a parent gets upset with a child for behaving in a careless and dangerous manner, the intensity of their reaction is due to the moral foundation of harm and care underwritten by our survival sense related to the moral foundation function and problem solving.  It’s role in moral foundations is similar to the g factor (Spearman, C. 1904) found in the major subtypes of intelligence.
Two other contemporary examples of prescriptive judgment regarding welfare: when authors in the New Atheism tradition attack religion on the grounds that it is harmful, they are implicitly also saying that the design of religion is, in total, wrong minded and ultimately misguided, they are motivated by the primary moral foundation function / problem solving.  And when, you, JH, seek to increase the sympathetic understanding of liberally minded folks of the moral motivations of their conservative counterparts, you too are motivated by this same ancient moral inclination.
We know that the judgment of function / dysfunction is intuitively moral because of the way emotions like disgust and anger attend the actions of others when they are deemed “dumb,” “thoughtless,” “ignorant,” “blind,” or “misguided.” 
  This moral foundation is related to the intellectual abilities of planing, problem solving, and tool making.  Problem solving and tool making is seen in apes and non-human species (Emery and Clayton 2004).  It is the basis for the enhanced reproductive survival of human beings. 

Christopher Lipp argues that Authority is not a foundation of morality; rather, hierarchies perform the function of supporting other moral foundations:

First, I begin by asserting that development along a single moral perspective demonstrates behaviors that enlist both liberal and non-liberal (seemingly-conservative) attitudes.  Second, I suggest that authority/respect is morally represented through associations to other moral foundations.  Finally, I conclude that authority/respect is likely a developmental behavior pattern that originates in pursuit of other moral foundations and is not a self-standing foundation.

1. Although you partially dismiss differences among moral development stages in pursuit of a single moral foundation, this dismissal may be premature.  One observation comes from Stephen Thoma's work using the Defining Issues Test to measure (Kohlberg's) justice moral development.  Thoma specifically found that pre- and post-conventional stages of moral development showed high levels of humanitarian liberal perspective scores, whereas conventional stages of moral development show a significantly less liberal perspective.  Along a similar vein, pre- and post-conventional stages of development showed significantly less religious orthodoxy than did conventional stages. 

If we consider Justice to be a single moral module (perhaps fairness/reciprocity) that develops along a continuum, then we must conclude that less-liberal attitudes (a focus on what appears to be desire greater security, i.e. conservative orientation) is merely a stage of development for fairness/reciprocity. Kohlberg's development has demonstrated cross-cultural stability with only minor exception in the realm of post-conventional stages; therefore, at least in part, Kohlberg has hit a singular moral foundation in which certain liberal behaviors and non-liberal conformist behaviors alike are encapsulated.  (Other evidence can be provided by request)

2. Looking at authority/respect as a conservative value, it appears much of your evidence supporting authority rests on the existence of hierarchies within primates and perhaps other animal species.  First, it is important to acknowledge that the existence of equivalent behaviors between humans and other animals is not a sufficient condition for morality.  We know, for example, that humans and mammals both demonstrate anger, yet humans distinctly show both moral and non-moral anger responses.  (a great paper on this is Gutierrez & Giner-Sorolla's 2007 article in Emotion).  Therefore, the question becomes: under what circumstances is authority demonstrated to be a moral foundation? 

Looking at authority/respect within the domain of Confucianism, here are summaries on both Confucius and a disciple, Mencius:

http://en.wikipedia.org/wiki/Confucius
While Confucianism generally regards rulers highly, he argued that it is acceptable for the subjects to overthrow or even kill a ruler who ignores the people's needs and rules harshly. This is because a ruler who does not rule justly is no longer a true ruler... All relationships should be beneficial, but each has its own principle or inner logic. A Ruler must justify his position by acting benevolently before he can expect reciprocation from the people.

http://plato.stanford.edu/entries/confucius/
Confucius' political philosophy is also rooted in his belief that a ruler should learn self-discipline, should govern his subjects by his own example, and should treat them with love and concern. “If the people be led by laws, and uniformity among them be sought by punishments, they will try to escape punishment and have no sense of shame. If they are led by virtue, and uniformity sought among them through the practice of ritual propriety, they will possess a sense of shame and come to you of their own accord.” (Lunyu 2.3; see also 13.6.)http://plato.stanford.edu/entries/confucius/

For Confucius, what characterized superior rulership was the possession of de or ‘virtue.’ Conceived of as a kind of moral power that allows one to win a following without recourse to physical force, such ‘virtue’ also enabled the ruler to maintain good order in his state without troubling himself and by relying on loyal and effective deputies. Confucius claimed that, “He who governs by means of his virtue is, to use an analogy, like the pole-star: it remains in its place while all the lesser stars do homage to it.” (Lunyu 2.1) The way to maintain and cultivate such royal ‘virtue’ was through the practice and enactment of li or ‘rituals’—the ceremonies that defined and punctuated the lives of the ancient Chinese aristocracy. These ceremonies encompassed: the sacrificial rites performed at ancestral temples to express humility and thankfulness; the ceremonies of enfeoffment, toasting, and gift exchange that bound together the aristocracy into a complex web of obligation and indebtedness; and the acts of politeness and decorum—such things as bowing and yielding—that identified their performers as gentlemen. In an influential study, Herbert Fingarette argues that the performance of these various ceremonies, when done correctly and sincerely, involves a ‘magical’ quality that underlies the efficacy of royal ‘virtue’ in accomplishing the aims of the ruler.

In essence, the categorization of moral virtue regarding authority in Confucianism is explained in terms of harm/care, fairness/reciprocity, and purity/sanctity.  This, in my experience, has been the defining nature of why people enter hierarchies: hierarchies perform the function of supporting other moral foundations.  Humans have hard-wired behavioral patterns that demonstrate hierarchy within a collective (as do other animals), yet I do not see evidence of a jump from having the hierarchy/authority behavior pattern to assuming that the behavior pattern itself becomes a moral end or foundation.  Rather, what I observe is that the authority/respect behavioral pattern takes on a moral valence as a result of associating the accomplishments obtainable through authoritative structures to care and justice, and by having the practice of kings and authority figures being tied to Divine Rights or Mandates from Heaven (Divinity/Sanctity).  It is also questionable whether duty is partially inspired by group loyalty. (I know of no moral support for a hierarchy that is not associated to the accomplishment of other foundations)

3. Returning to developmental patterns, Kohlberg would perhaps argue that different stages of development enlist different patterns of behavior in order to support the primary orientation of Justice.  These behaviors are sometimes liberal, sometimes not.  Hierarchy is a behavior pattern in humans, and therefore quite possibly enlisted in pursuit of achieving other moral foundations.  I consider it a high probability that the moral foundation of authority/respect is a behavioral pattern adopted to support other pre-existing moral foundations (and likely coincides with a particular developmental stage of those foundations) .

Michael Sinding proposes that LIFE, and FEELING might be foundations: [submitted aug. 13, 2009]

1) Life: We generally feel happiness at life and birth, and sorrow at death and dying. This has an obvious evolutionary motive. There are all manner of symbols and rituals relating to fertility, and similarly to death and killing. We defy our fear and hatred of death with beliefs about life after death. Life is mentioned as a ‘sacred value’ in “Moral Foundations of Politics” (1036)). This doesn’t fit neatly into the other Foundations. Killing may be seen as wrong for various reasons: because it’s unfair and harmful, and (generally) forbidden, but also because it contravenes individual liberty, and sanctity. All these values and reasons may be involved in debates over abortion and euthanasia and eating meat. Consider another example: I think people would disapprove of suicide (and of assisting it) if it was not motivated by some strong moral reason, even if it were painless, clean, and didn’t harm others in any way. More generally, people feel disgust at unnecessary killing.
As for a mechanism of life/ death detection, I believe we have ways of perceiving something animate from the way it moves. For inanimate beings (i.e. plants), we perceive signs of life in colour, texture, smell, position (i.e. dead plants do not support themselves). Like the other foundations, it seems only to divide liberals and conservatives when push comes to shove, and as other foundations get involved. There is lots of disagreement on whose and what kind of life is a value, and why, and how much, and in what circumstances.

Given that the foundations are themselves emotional and intuitive, taking feeling as a foundation makes it reflexive in a way: feeling about feeling. That’s as it should be, because emotions are important in social life, communicating information (e.g. fear and screaming = danger), but also causing feeling in others (happiness, fear, hate, etc. can be ‘contagious’). This is not the same as harm/ care, because that foundation seems focused on physical feeling, and does not seem to say much about favouring positive feeling. As for mechanisms of detection, obviously we have direct access to our physical feelings of pain and pleasure, and we seem to have direct access to our own emotions (though as they get more complex they get harder to recognize and understand). When it comes to detecting feelings and emotions of other people, Theory of Mind is probably involved, with whatever further explanation we would like to add for that capacity—e.g. simulation, based on mirror neurons.

[Comment from Haidt: this is a very different way of dividing up the "foundations" of morality, but these seem plausible as special, structured-in-advance-of-experience sensitivities which contribute to moral judgment]

Daniel Schut, from Amsterdam, proposes that Max Weber's three sources of legitimacy provide an alternative way to analyze moral reasoning: [submitted April 2, 2010]

I believe that we can best describe the foundations of morality by using a modification of Weber's 'sources of legitimacy'. Importantly, these categories do not describe 'ultimate sources', but describe 'modes of reasoning': they point us towards what a certain person might find acceptable grounds for a moral argument or not.

To wit, Weber's three sources of legitimacy were:

- Rationality
- Authority/tradition
- Charisma

If you'd view 'rationality' as 'using rational arguments', i.e. arguments that can be explained and reasoned through via mutually acceptable propositions that have a claim to universal validity. Both deontology and consequentialism would fall under this category. This category would be called 'public reason' by Kantians like Rawls. Your category of harm and fairness would both fall under this category.

Authority/tradition are all arguments that are based on the integrity of social constucts, i.e. arguments based on the integrity of the group, or the integrity of the hierarchy of the group. Both authority and ingroup-loyalty would fall under these categories. They differ from rational sources because the social constructs can, by their nature, not make a claim to universal validity: the integrity of someone else's group will have no or little moral force for me when I'm not a member of that group.

Charisma originally referred to 'the inspiring leader', but in my mind should be redefined as moral reasoning solely based on emotions, and more specifically, the emotions of elation and joy, and the opposite emotions of anger, resentment and disgust.

With these three categories, there's three types of moral reasoning.