Absolutely. Most notably there was a group in the area known as the Cochranites, more formally The Society of Free Brethren and Sisters. They practiced a marriage tradition they called "Spiritual Wifery" in which wives were assigned to men based on the whim of the leader Jacob Cochran. Evidently the assigning of wives could and would be changed frequently. At one point Cochran himself was married to roughly half the women in the church.

Eventually Cochran was tried and convicted of "gross lewdness, lascivious behavior, and adultery," for which he served four years in prison. The church largely disbanded while he was serving his prison term. However the LDS church was formed geographically close to where the Cochranites were established, and several former Cochranites joined the LDS church. Lyman Wright was even ordained as an Apostle in the early LDS church. At several times the LDS church preached against "spiritual wifery" to distance themselves from the Cochranites. Even when polygamy established and openly admitted, Brigham Young and other leaders took pains to differentiate themselves from the Cochranite practice. None the less several contemporaries drew parallels between the earlier Cochranites and the later Mormons.

That's the most clear connection. But there were other religious groups which practiced non-traditional marriage or sexual practices in the area. For example the community of Oneida had a universal common marriage, or more properly a complete renunciation of marriage, in which any adult man and woman could engage in sexual intercourse. But they weren't supposed to procreate. So men who hadn't learned to control their ejaculation were only allowed to have sex with post-menopausal women who couldn't conceive. Younger fertile women were only to have sex with those men who had learned the group's method of ejaculation control. Outside that anyone could partner with anyone they pleased. But close "possessive" feelings were discouraged. Community members were encouraged to sleep around rather than pair off. Such a large open set of relationships isn't polygamy, but it is one example of the type of experimentation that was going on in the Burnt Over District in the early 19th century.