It is useful to review the answers to a prior question about Sam Harris: Is Sam Harris's view of morality innovating? What philosophers innovated specifics on morality? Harris is not a well informed philosopher, and does not provide anything near to a coherent argument in support of his claims. I make the same point in a review of his book, the moral landscape: https://www.amazon.com/gp/customer-reviews/R3SB3ZQ7Y8SX1Y/ref=cm_cr_arp_d_rvw_ttl?ie=UTF8&ASIN=143917122X Harris is GROSSLY uninformed about philosophic thinking about morality, and the difficulty of getting from "is" to "ought". He substitutes question-begging rhetoric and undescribed assumptions for reasoned argument, and is unaware that anyone can or does reject his assumptions (which primarily consist of utilitarianism, scientism, and material reductionism, without recognizing that neither values nor consciousness even exist in a thoroughgoing material reduction).
There ARE ways to get to empirically supported ethics -- but they must operate out of pragmatic worldview, not the logical positivism of Harris, as empiricism is based on INFERENTIAL JUDGEMENT, not closed form logic. And pragmatic reasoning can never provide the certainty that Harris claims.
For some examples, Darwinian ethics and Deep Ecology offer ways to do ethics empirically. Darwinian ethics have historically celebrated dominance and Alpha-male behavior, based on their survival advantage, which most other ethicists consider UN ethical. See the author's POV in https://www.amazon.com/Sperm-Wars-Infidelity-Conflict-Bedroom/dp/1560258489 for an example of rationalizing alpha dominance and rape and infidelity, based on the presumption that their role as successful reproduction strategies in human evolution justifies these practices (conflating "is" with "ought").
An alternative Darwinian approach is to note that humans are more Eusocial than most species. And eusocial species are dramatically more successful than most species. But Eusociality requires that members of the species generally put the good of the community ahead of their own welfare. If this is an essential human trait that has lead to our success in the world, then morality is reasonably an evolved inclination that is essential to human survival and success. This is a darwinian/empirical approach that at least approximates moral thinking, AND tries to get to "ought" from "is" with consequentialist justifications.
Deep ecology applies utilitarianism to ALL of life, arguing that we are the reasoning part of Life, and must act to guide Gaia, for when natural processes fail Her welfare. This is not empirical, but is explicitly consequentialist, which is closely related.
Within each of these views, there can be empirically based detailed rationales, but the validity of any such argument, requires that one accept the larger worldview they are framed in.