I'm pretty sure quad works - as Xeromag.com sums it up
QUAD: A polyamorous relationship involving four people, each of whom may or may not be sexually and emotionally involved with all the other members. See related N. Commentary: One of the most common ways for a quad to form is when two polyamorous couples begin romantic relationships cross-couple
My OKC profile lists me as available (you can put you're not single but check the boxes that you are looking for long or short term dating or casual sex, which switches your label to available) In my first paragraph or two I state that I'm married and that I have another relationship too. I mention polyamory. When my husband has his profile active, I include a link to it so they can look at see who he is and that we both are on the same page. I always like it when people (especially men) do this, it lets me see that everything is above board and erases concerns they are cheating, and I can get a better feel for the sort of relationships they form. My advice is to browse other people's profiles with a keyword search for poly/amory and see how different people present the information.
In general people don't like finding out you already have a partner after you meet them. Giving them the info ahead of time lets them make an informed choice about whether they want to fit into what I have going on. And of course lots of people are not open to that, but depending on where you are, the dating pool can still be very large. If you want to date people who aren't identified as poly you can use open or non monogamous to describe your relationship too if you prefer - lots more people have a general idea what that is than will be familiar with poly. Just fill out the details about the specifics of your relationship in further conversation.
On that note, my strong advice is to NOT date anybody who doesn't already identify as poly or open right away if there are available interesting poly people in your area. That comes with a whole lot of problems that I think are generally best avoided until you've figured out what you want and have experienced the initial stuff inherent in changing your dynamic. Lots of people would not give the same advice, but it can be less confusing to (for both you and them) to date somebody who already has a clear understanding of what poly means to them - even if it differs from what poly means to you. It's also more likely they'll be understanding about the road bumps that can happen as you and Kas negotiate all this for the first time, because they've been there.
There are some threads on here about how to broach the subject with people you meet say - at a bar or party or work when you don't know if they are open to poly or not. I'd direct you to find them, as I haven't been single for 20 years, and never approached somebody who I didn't know was already poly for the purpose of dating.
And likely reading those books will help Kas with some of the guilt or weirdness about it. So will meeting other poly people and discussing things with them. It helps to spend time with like minded people, it makes you feel like you're not abnormal for choosing non-monogamy. (That's also one benefit I find likely for her with dating already poly people - people who aren't can be kind of shitty when you tell them about being open - they often make lots of wrong assumptions about you, which would reinforce the feeling that you're doing something "wrong".)
Happiness will never come to those who fail to appreciate what they already have.