Fiats with god and commandments won't count for you then.
I would relate the core of our moral reasoning and behaviour to intersubjectivity, like the most cross-cultural moral guide nicknamed the Golden Rule, often framed as 'Do as you would be done by'. Intersubjectivity supports learning and language use, and those we don't extend it to we effectively treat as objects, or as means not ends. Discussed here: Is the Categorical Imperative Simply Bad Math? :) The binding in this context is how we extend our own minds by treating others as like us, like say relying on their reports or experimental results as though we were in their shoes.
The idea we have a social contract, us one way of thinking. If someone violates the expectations of the community, they get exiled (like Atistotle), or imprisoned which seperates them from the community. Participation involves committing to obeying laws and social norms like that demonstrate you are a morally responsible persin, and the penalties for failure are various kinds of exclusion, and sometimes punitive measures. Rioting or revolution express a widespread sense the social contract is being violated, or needs to change.
Durkheim had another way of framing this, that the binding is around the 'enactment of shared attitudes to sacred things' resulting in social cohesion around them, and the absence of those results in anomie, puposelessness and negative feeling associated with lack of connections to others. Note enacted means not only asserted, but celebrated, paryicipated in. His framing can take in religions not just of the Abrahamic kind, but yogis, Shinto and shamanism, and also around codes like no-detention-without-trial, or the scientific community around the values of scientific method. The binding power is resisting anomie.
Moral Foundations Theory and the research it's based on, seems to indicate that we have 'moral drives', like for justice/fairness, because they enable human cooperation, which is so advantageous we develop mechanisms of peer-pressure and legal enforcement to manage tensions that would arise from people violating them without consequences. It should be noted that a small fraction in all societies exhibit psycopathy and can't be relied on to be governed by their moral intuitions, as well as people over-ruling their morality for the sake of other drives. The binding power here is evolved drives.
Nicholas Christakis talks about the evolution of a wider 'social suite' of behaviours that enable cooperation which seem to be the basis of our morality, in this podcast on Humanity, Biology, and What Makes Us Good. The binding power for him is how society and socialising well benefit individuals.
Patricia Churchland, has been developing the field of neurophilosophy. This specifically addresses the origins of moral intuitions, and of conscience. Discussed in this podcast: Conscience, Morality, and the Brain. The binding power here is brain structures and mechanisms.
It's interesting to note as well as what seems fairly universal, also how much humans vary around the world. Different balances of priorities, resulting from different historical contingencies. This is especially apparent around obscenity and pornography law differences, discussed here: Is artificially generating images of minors in sexual positions unethical? We can think of cultural norms as relating to game theory equilibria, which may be more or less srable, and have more or less mutaul benefits from maintaining them. Discussed here: Is the tyrannicide perpetrated by William Tell morally legitimate? Like it's interesting to note that in many ways Ancient Roman society was like ours but, the idea of making slaves fight to death for entertainment was not considered immoral. The group of moral concern was limited to Roman citizens. The binding power of game-theory derived morality is the benefits of maintaining unstable equilibria.
Peter Singer uses utilitarian thinking, to argue that abolishing slavery, and expanding sufferage and citizenship to the whole community, means expanding the 'circle of our moral concern', and that to do so represents the direction of moral progress, which in future should encompass animals. The binding power of this picture is from identifying a direction of positive development, which surely we will want to align with.
Intersubjectivity, enhanced cooperation by keeping to a social contract, and increasing the circle of who is a moral subject, can be linked together like in this answer: Studies exploring the rationale of gender equality as increasing a societies capabilities.
Joseph Tainter looked at the collapse of complex civilisations, and concluded that challenges like caused by resource depletion do not hit steadily, and result in sudden demands for increased human cooperation, or we face 'rapid simplification' of our living standards which is to say collapse of a society or even civilisational collapse, if we cannot face a new major challenge. Perhaps this is the real backstop to morality as systaining cooperation, we get benefits for cooperating, and they are all in the line if we can't ratchet up our ability to do so.