Germany is such a country. However, as part of granting you citizenship they do a search for other countries that you have citizenship of. I believe they will not grant you German citizenship until you have relinquished your other citizenship.

I suppose another test case would be if you were to apply for German citizenship following your unilateral renunciation.

You can get double citizenship in Germany by birth and if the other country does generally not grant loss if nationality. Some other exception I don't recall by heart, but generally not.

And nowadays without difficulty if the other country is a EU country. But that is a deviation from German law tradition EU has forced on them.

If you had to give up any other citizenships first, then you'd be temporarily stateless. And then what if Germany decided not to make you a citizen after that? Where would they deport you to?

Statelessness exists, but the UN treats it as a human rights concern so I doubt Germany would impose it.

The way it works in Austria, another country that only allows single citizenship is as follows.

You apply for Austrian citizenship while you still have your original citizenship. Austrian authorities decide whether or not you should receive citizenship, *but do not grant it to you*

Instead they give you documents that basically say that you have an entitlement to Austrian citizenship the second you renounce all other citizenships, if possible. There are exceptions for some, none cooperative nations.

So if you are a US citizen you would basically have a document that says you are an Austrian citizen the second you renounce your American one. I imagine the Germany handles it similarly