The restriction to look at now is whether the marital status of each spouse in the marriage at hand is single. Today it has to be. But there's not a good reason for it. (As already mentioned, administrative convenience is not a good reason). So why can't Alice, who is married to Bob, now also marry Carol? Bob isn't marrying Carol; the A-C marriage would be between two people only. You're treating Alice differently merely because she is already married.
So what happens to Alice's stuff when she dies? How are property rights naturally divided? I can tell you there would be different interpretations of what happens and that's a problem. You need new law or legal precedent to establish how that works.
Sure, it's not intractable, it's also not even something I'd be against. Equal protection, however, is based on "protected classes" and the state of "being married" is not one of those. Why should it be? Someone who is married is denied the joys of