For example, immigration sponsorship. As a gay man with a non-American partner, this comes to mind first.
Currently, spouses do not have to testify against each other in court. This isn't codified in any law but British Common law (afaik). There are a few of these pleasantries that would have to be figured out.
Then, there are over 1,000 legal rights codified into contract law. Some of these can be emulated (power of attorney), some cannot.