Do any countries allow most cases of dual citizenship, yet somehow restrict triple citizenship?

Question

Are there any countries in the world that, in the general case, act to restrict or discourage triple citizenship, but not dual citizenship? That is, is there a country for which the following are actually true:

1. The country does not act to restrict, restrain, or punish citizens who are holders of exactly two nationalities, or to prevent citizens from acquiring a total of two nationalities. (For example, by causing the citizen to lose their citizenship.) This must hold for most possible second nationalities.
2. The country does act to restrict, restrain, or punish citizens who are holders of more than two nationalities, or acts to prevent citizens from acquiring three total nationalities. This must hold for most possible third nationalities.

I ask because I've seen many people with the idea that dual citizenship and triple citizenship might be treated differently, but never any evidence that this actually happens. In Cabo Verde, for example, many people believe that one can have dual citizenship with the US, but not triple citizenship if the US is involved, but this is in principle false.

Answer 1

Yes, at least one country does, Uganda.

At least according to the Government of Uganda website: https://www.gou.go.ug/content/ugandan-citizenship

DOES DUAL CITIZENSHIP INCLUDE POSESSION OF THREE CITIZENSHIPS?

NO; dual citizenship in Uganda means only two citizenships of which one is Uganda. The possession of a third citizenship disqualifies one from holding or being a dual national of Uganda unless the third citizenship is renounced.

This seems to be supported by Section 19E (page 9) of the Citizenship & Immigration Control Amendment Act, 2009.

19E Termination of citizenship of Uganda

For the avoidance of doubt, where by virtue of the holding of dual nationality granted under Section 19A or 19B, a person holds the citizenship of Uganda in addition to the citizenship of another country, the board may by order deprive that person of the citizenship of Uganda -

(a) upon any of the grounds specified in sections 17 or 18; or

(b) if that person acquires a third citizenship

Emphasis mine.

Answer 2

I can't prove a negative, but basically, no, the only meaningful distinction is between "one citizenship" and "more than one".

By and large, the countries of the world fall into two camps:

1. Having another citizenship is OK.
2. Having another citizenship is not OK, and we'll take away ours if you get one.

The countries in the first camp do not care how many citizenships you have. And the countries in the second camp also don't care, since any number over one is enough to cause you to lose your citizenship.