It is de facto and/or de jure legal to have relationships with multiple women in all US states. What's not legal is having multiple licensed marriages.
To expand on what
@steve and
@Verifyveritas76 were saying, you can do inheritance anyway you like. The only thing a lack of legal marriage means is a mans property won't pass to his wife by default. But since you'd have multiple wives, that won't work anyway. A will will get it done however you like. But Trusts are better because they avoid probate, which can be messy and expensive.
Tax...only 1 person will be able to claim them as dependents. And the man will only be able to file jointly as married with his legal wife. Others would have to file singly. But ask a tax pro to be sure. Is the marriage penalty still a thing? Not being able to claim legal marriage status may only help.
Health insurance is more complicated. Anyone can purchase but with the federalization it is crazy expensive. Insurance through the workplace is likely only going to be good for the employee and their legal spouse, not any sisterwives or the husband if a non-legal wife is the employee. Kids...will depend on the employer; but they're getting more and more picky about proving the dependents are yours so you may find you can only insure children who are biologically yours. Medical sharing ministries may be more lax in this regard, and are cheaper, but they often have morality clauses which are likely to cause problems for polygamists (or at least they did in the past).
then additional wives who have no legal contract
No legal marriage license. But it is common for people to have cohabitation agreements; which are a legal contract. They're not too dissimilar to a rental agreement. I've also toyed with the idea of organizing as an intentional community. It is not uncommon presently and historically for those to practice some form of plural marriage and they fall under the same sort of tax and org law as monasteries. These will also often hold real property in trusts.
Trusts are a very powerful tool. And they're not just a place to park assets. They can get bank accounts, act as a tax vehicle, etc.
disclaimer: I'm not licensed by the government to tell you any of this, if you get serious about this find someone to give you a 'legal' opinion.