Multiple instances of the same DbContext with different connection strings

I know this is more like a howto question and should be asked on StackOverflow. I did ask here: https://stackoverflow.com/questions/45724257/asp-net-core-with-separate-databases but it seems like there are not too many experts being able to answer this. Maybe someone here can help.

My ASP.NET Core 2.0 application must support multiple databases. Which database is to be used should depend on the ApplicationUser issuing a request on a per-request basis.

That rules out AddDbContext in Startup.cs with a single connection string (there will be multiple connection strings in my application.json file).

A multi-tenant approach as described here http://benfoster.io/blog/asp-net-5-multitenancy seems to be too restrictive because I actually don’t want complete isolation. There will be users (managers etc.) that should be able to switch between databases. Normal users will be restricted to one specific database. Apart from that I thought I could manage this without third party code.

I found this https://github.com/aspnet/EntityFrameworkCore/issues/6863 which seems to be related.

Note: I don’t need multiple instances of the same context in my controller, as discussed here https://github.com/aspnet/DependencyInjection/issues/352 I just need the correct one depending on the user.

In my SO post ‘poke’ comments:

Database contexts are usually configured to be created once per every request, so the configuration can change on a per-request basis. You just need to come up with a nice way to configure the contexts depending on your user … So you should use a single database context but just make sure that your DbContextOptions configure the correct connection string per request. Or put the logic inside the db context (ugh though) by overriding OnConfiguring

So how do I use DbContextOptions to realize this?

I would be thankful for every hint!