Name a country that has been colonized by two or more other countries at any time in its history.

I beg to differ. MANY existing countries have been colonized, and yes, often by way of invasion. It's the invaders themselves who disavow recognizing the existing sovereignty, but that doesn't mean they're correct in doing so.
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Out of interest, can anyone name any country in South America that was colonized?

There is no place called "Britain". The British Isles have always been called "The British Isles". Nobody knows where the name came from, but some students point out that "brit ish" is Hebrew for "covenant man" which lines up with their theory that the Jewish king line has been preserved there. It seems that "Britain" was back-formed from "British" to get the current name, The United Kingdom of Great Britain And Northern Ireland. But in any case, those colonizations took place before the nations existed.

Britannia. Roman colony. Study a little history. Possibly derived from the Greek Prettanike, "painted folk", but that referred to the population rather than the place which was called Albion.
Britannia also only referred to that part of the island south of Hadrian's Wall. Scotland was known as Caledonia,  Ireland as Hibernia. England per se didn't exist at the time, the Angles who caused it to be named "Angle land" hadn't got there yet. 

Britain, a widely used short-form for 'Great Britain', by we people who live here, is not congruous with 'British Isles'. The 'United Kingdom, is a further separate distinction. The vast numbers of books written about the Roman invasion of Britain would tend to make nonsense of your brave assertion.. This post was edited by TONEALONE at January 22, 2018 8:00 AM MST

It is unfortunate that you let that slip out because by any standard it is false. Perhaps you gleaned it from the Internet. If so, another warning for would be knowalls using a brain remote from their own actual person. The British Isles is a geographical distinction, not a political one. It includes Southern Ireland or Eire, most of whose population would not thank you for asserting their country is, in fact, part of Britain. Northern Ireland IS British, by persistent democratic choice, but the majority of the Island is not British and owes no allegiance to the British crown.  

https://groups.google.com/group/alt.history.british/browse_thread/thread/9d0a33cf1fbcbc1a/ec69d4e4d44f9daf#ec69d4e4d44f9daf

 

Scroll down to "Don Aitken".

The Filipinos made a colony at Morro Bay, California! That was October 18, 1587. They came on a Spanish ship. It sounds like they weren't really serious.

Africa is not a country. It is a continent with one fifth of the world's land, one sixth of the world's countries, and one seventh of the world's population, speaking up to 3,000 languages depending on how you count. Africa is this big: 

This post was edited by Not Sure at January 21, 2018 9:16 AM MST

I said SOUTH Africa, which is certainly a country. Has the unusual distinction of having its executive, legislative and judicial capitals in different cities - Pretoria, Cape Town and Bloemfontein, respectively. History mired in bloodshed, violence and gross injustice (the Boer War with its concentration camps, then Apartheid).