In fairness, the "Nashville Statement" is in toto
an Evangelical Fundamentalist document and not reflective of mainstream American Protestant Christianity. Several major mainstream Christian denominations have endorsed gay marriage - Episcopalians, Presbyterians, the United Church of Christ, and some Lutherans - as well as other less mainstream Christians such as the Quakers, the New Thought churches (such as Unity and Religious Science) - and, of course, the MCC.
However, even the mainstream denominations that have endorsed gay marriage are undoubtedly a long way from endorsing polyamory. As an exception, the MCC does specifically endorse polyamory in their counter-statement to the "Nashville Statement" -
Additionally, the New Thought churches and the (non-Christian) UU Churches are welcoming of poly folks as well.