Can we both file head of household?

My SO are talking about getting married, and not that this carries and weight but I’m curious. We each have our own homes (mortgages), due to kids and where I work (closer to his house) we have talked about keeping our current arrangement. Currently we have almost opposite custody schedules so my house when I have my kids and his house when he has his kids and when we have no kids. Someday we’ll buy a house together but we both have small mortgages (thanks Covid interest rates!) so no rush. Anyways since we will both have our own houses and spend slightly more than 50% of the time at our respected houses (logistics won’t allow us to spend every night together) would we both be able to file as “married filing separately” and both claim head of household? We both have our own house and we both claim our own kids.