Can a researcher work full-time in two universities on a rotational basis?
For instance, say someone works in a university 'A' in Europe from February to May and then works in a university 'B' in the Middle East from October to January, etc.
Is it possible?
Has anyone done that before?
I take your question to mean that you want two part-time jobs at different universities that together form one full-time job. If you want two full-time jobs, then forget about that ( How to get two paid affiliations? ).
Unlike Wolfgang I do think that it is possible without first winning a Nobel prize. Some countries (like the Netherlands) are much more flexible when it comes to part-time work than others (like Germany). It possible to find two part-time jobs in two flexible countries and make good arrangement with both universities to make that work. However, it is not easy:
Financially, you should expect such an arrangement to be a loss. In terms of time and effort, you should expect it to be a loss. You need to have another very strong reason for accepting those losses. For example, I have seen such an arrangement for international couples who want their children to fully experience both cultures.
Anything can be done as long as it does not violate the law. In your case, you just need to find two employers who are willing to give you a job contract that allows for what you propose -- namely, a contract that pays your for six months of work per year, and gives you unpaid leave for the remainder of the year; or a contract that pays you for 50% work throughout the year, with the expectation that you spend 50% of the year on location.
Is that practicable? That is a question that depends on the person and the universities involved. If you have received a Nobel prize, then you can negotiate pretty much whatever you want with any university in the world because they will be eager to have you on their faculty, and I suspect that a fair number of Nobel prize winners have exactly the sort of arrangement you suggest. If, on the other hand, you're a second year faculty at Podunk State University, with ten publications and 200 citations, then you probably don't have the negotiation power to do that: If you go to your department head and ask whether you could go to a 50% position where you're only going to be in town for six months of the year, the department head will likely say "That is not worth our time and money; we wish you well should you decide to go that other university on a permanent basis".
Full time in separate countries? Seems unlikely but not impossible (see Wolfgang's answer). I do regularly see people with joint appointments, usually at a research focused location and another at a university. Where the second is there to do teaching and possibly comply with regulations for having students. But this is usually in the same country and same city (or at least having the locations near each other).
The other option is taking a sabbatical. Where you may still be paid by your normal university, but get to go spend a year doing other stuff, possibly at other universities. You could then structure that to spend 6 months in Europe and 6 in another country. But this would only be a temporary arrangement.
