How old are your kids? Mine were 7 and 9 when we split. My ex and I nested the children so they stayed in the home while we moved in and out. He lived with his new partner half the week and I lived with mine the other half. My dining room had a good sofabed and a chest of drawers for him while he stayed so he didn’t use my private space. This wouldn’t work for many couples but it worked for us for a number of reasons:
We have very similar views on parenting and even though we didn’t get along as a couple (we split because he realised he was gay) he was a fully present and active coparent - arranged and did his fair share of doctor/dentist appointments, shopped and cooked on his days, did equal school/club/activity runs, did the kids laundry, etc.
Financially generous - when we lived together we had a joint account for bills and mortgage and he continued to pay his full half after he moved out.
We got along with each others new partners - and they weren’t jealous/possessive/weirded out by the situation. We’ll never be besties but we can have a pleasant chat when we meet each other.
It was unusual and it was a privilege to be able to do this. My ex and I thought very carefully about it and had a relentless focus on putting the kids front and centre of any arrangement, even if it inconvenienced us. The kids stayed in the same house, went to the same school, did the same clubs and to be honest, I think they would tell you their lives didn’t change that much. My partner came with me when it was my turn to be in the house and it all just became a normal routine. If anything, my DD jokes that she has one mum and three dads. My DP has been great with the kids and they love him which also helps.
The kids are adults now. My ex and I are divorced and my DP and I bought him out of the marital home.
I’ll be honest and say that it took a lot of energy and effort for me to push us down this route without getting angry and bitter, especially in the early days (it wasn’t how I anticipated my life or marriage in my 40s) but it was worth it.
Edited to add: the kids had access to both of us even if we weren’t the resident parent. I’d pop in after work if I was needed for something and vice versa, and they could FaceTime or call whenever they wanted.