I cannot seem to get this to work if both identities are in the same domain.
For example, I have a regular login, richard.d.lawson@willistowerswatson.com, and an account with elevated privileges, richard.d.lawson_ELEVATED@willistowerswatson.com. I cannot get the Azure portal to log in with my second account. It keeps only logging me in on my regular, unelevated account.
It's not a problem with the elevated account because if I use another browser and only ever log into it with my elevated account, I can log into the Azure Portal. It's only when the Azure Portal tries to use both my elevated and unelevated accounts at the same time that it balks and only allows one account to log in.
For now the solution is to use one browser for one account and another browser for another account, but that is very annoying.