US/UK Citizenship -more time in the EU?

Perhaps a bit off topic so please forgive me.
For anyone who has dual US / UK citizenship wanting to stay longer than 90 days out of 180 days in the EU (since Brexit rules started), does anyone know if it is possible/legal to travel to EU on UK passport and  stay for 90 days, return to UK and rather than wait 90 days to return to EU on UK passport, travel back straight away with US passport ie 90 days on UK passport, then 90 days on US passport and repeat.

Perhaps a bit off topic so please forgive me.
For anyone who has dual US / UK citizenship wanting to stay longer than 90 days out of 180 days in the EU (since Brexit rules started), does anyone know if it is possible/legal to travel to EU on UK passport and  stay for 90 days, return to UK and rather than wait 90 days to return to EU on UK passport, travel back straight away with US passport ie 90 days on UK passport, then 90 days on US passport and repeat.

I expect it's like every other rule dodge, someone may get away with it once or twice but I can't imagine it's legal.

It sounds like you want to spend a lot of time in the EU country, have you looked into obtaining a resident visa?

Only you can decide if you want to risk exceeding the 90 days in any 6 months.
https://www.schengenvisainfo.com/consequences-of-overstaying-in-schengen-area/

I expect it's like every other rule dodge, someone may get away with it once or twice but I can't imagine it's legal.

It sounds like you want to spend a lot of time in the EU country, have you looked into obtaining a resident visa?

I agree with Larabee.  Chances are you’d be able to get away with it, at least for a bit (assuming no rule breaking like working or anything).  But, if you have a second home or something specifically drawing you to another country, I’d explore more robust options. 

What will you do for healthcare cover? British citizens can only use the NHS bill free if they can prove they are residing in the UK (exemptions for certain people such as those with the AF, crown servants posted abroad etc). The NHS bill will be 150% of the national cost. For NHS England, you will need to pay up front. British citizens had to be living in the EU before the 1 January 2021 to be able to use the NHS without being billed

All the EU countries have insurance based healthcare systems to fund those living in their country. It might be hard to find a travel insurance policy that will pay out on any overstaying?

The EHIC is only for visiting and is limited in what it covers, which is why we also need travel insurance too, which might not pay out for overstayers
https://www.gov.uk/guidance/uk-residents-visiting-the-eueea-and-switzerland-healthcare

Many thanks for your replies.