Some of the interpersonal relationships in Emily's other world are straightforward enough, others seem strange. Three-way marriages were apparently quite normal in Emily's other world. In a three-way marriage, for instance, the new partner has exactly the same rights as the first two partners. When Paul married Janet and Eric, he had the same rights as they did. Being the first in a marriage offers no legal advantages.
Couples definitely give something up if they marry a third person.
Of course, they gain a lot as well. But most decide not to. Though legally valid, the ceremony does not affect either party's legal status. It's only purpose is to enable the individual to experience a marriage ceremony. Many readers will remember Emily's appearance on The Tonight Show with Johnny Carson.