Assume that a person (not me, I only hold a single citizenship :) has a double citizenship in countries such as the US, Singapore, Australia, Japan, etc, which are eligible for 90/180 visa-free stays in the Schengen area. Could they officially remain in the Schengen area indefinitely by taking a trip to (say) the UK every 89 days?
No, the logic is quite clear, the rule applies to a person. Having several short-stay visas from the same or from different countries in the area would not help either, the visa conditions (including whether you need one or not) and the duration of stay are two separate things.
Formally, it would however seem possible to alternate between three months in the UK and three months in Schengen area indefinitely, even with only one citizenship and multiple entry visas for each country. But border guards in either the Schengen area or the UK could still become suspicious about the real purpose of your stays.
Legally, no, the rules are for a single person.
Practically speaking, you could probably get away with it though, because visas and databases assume that passport equals person -- although if anybody ever does get suspicious, it wouldn't take long for them to figure out that there's a clone with the same birth date and biometrics.
Is possible, I have been doing this for over a year, I'm holding two passports, and in most of the boarders they dont check your dates, even in Denmark or Sweden... I had some questions in Portugal, and I finally got caught in Poland crossing from Kaliningrad, but they let me.go, because I'm not.doing any illegal thing... Since I have been out from schengen after 90 days with my passports and doing visa run. I was in the immigration office waiting for over hour while they were argue about my situation, but I didn't get any paper or report about it, and they came with me to the bus... The only advice that I can give is if you are travelling you need to this: Imagine if you need to ddo visa run after 90 days, you need to go to a country where you have a visa with the other passport... So you go out of schengen, stamp the first passport, then go to the next country and the get the stamp with the second passport, enter and exit, then go back to schengen... Is not suspicious because you are coming from a country that you already have stamp... But if it happen like.me that I went to Kaliningrad, I had to stamp my first passport because I didnt have visa with my second passport, so the exit from Poland was ok, and entry and exit to Russia the same, but when I tried to get back in poland they realized that I didnt have thr stamp from Russia, and in that boarder is the only country that you can come, so they asked me.for.my other passport and they saw all the time that I was coming and going from schengen... But as I said, I didnt have any major.problem and now I'm in schengen again...