In a way, this represents my idiosyncratic variant on Richard Joyce’s The Myth of Morality.

There are many Candidate Moralities: Kantianisms, Virtue Theories, Natural Law Theories, Utilitarianisms, and as many Common Sense Moralities as there are people with a mish-mash of intuitions and principles in their heads, which is to say, as many as there are people. But for the most part every Candidate Morality claims at least two properties for itself:

Universality (U): If a Morality dictates a moral obligation to φ, then every person, actual or potential, has an obligation to φ. (Note that “to φ” here can be to act or to refrain from acting).

Rational overridingness (RO): If a Morality dictates a moral obligation to φ, then it gives an overriding reason to φ to the relevant person who has the obligation to φ. An “overriding reason” is one such that if one can have such a reason to φ, then one must rationally φ, notwithstanding whatever other reasons one has to not-φ.

Combining U and RO we get a General Property of Morality or GPM:

(GPM) If a Morality dictates that φ, then that Morality gives every actual and potential person an overriding reason to φ.

If we propose a highly intuitive proposition called the Exclusivity of Overriding Reasons (EOR):

(EOR) If a person has an overriding reason to φ, then that person does not have have overriding reason to not-φ

then we can conclude

(GPM’) If a Morality dictates that φ, then there is no person with an overriding reason to not-φ

But I find at least two other propositions highly intuitive:

Rationality of Minimal Self-Interest (RMSI): If a person will suffer enough as a consequence of φ-ing, then that person has an overriding reason to not-φ.

and

Morality Always Screws Somebody (MASS): There will always be either an actual or potential person who will suffer enough as a consequence of φ-ing that they will have an overriding reason to not-φ. (As William Blake once expressed it, “One Law for the Lion & Ox is Oppression.”

but if MASS is true then GPM’ must be false, which since it is derived from U, RO, and EOR means that at least one of these must be false. EOR seems to be true almost by definition, so that leaves us with throwing out either U or RO, either one of which seems fatal for any Morality. Throwing out U leads (most likely) to some variant of moral relativism, while throwing out RO threatens to make Morality purely arbitrary, or simply optional.