`DbContext.Database.BeginTransaction` can't be nested?

I'm trying the EF6-way of using transactions and noticed that the following code

using (db.Database.BeginTransaction())
{
    // something
    using (db.Database.BeginTransaction())
    {
        /// something
    }
}

throws an exception on the second begin transaction telling me that

The connection is already in a transaction and cannot participate in another
transaction. EntityClient does not support parallel transactions.

Not that I would want to do a parallel transaction, whatever that could mean on one connection. I just wanted a nested one.

So is this indeed not supported on what's going on?