Is triple citizenship possible?

DS is a dual national, having been born in the UK to American mother, British father.  His girl friend was born in the US but her mother is Canadian and GF is about to seek Canadian citizenship.  Should they ever produce offspring, would that child be entitled to US/UK/Canadian citizenship?  Then, if I get Irish citizenship through a grandparent, would my future grandchildren be able to claim Irish citizenship?
Just wondered if this type of thing ever came up.  How far could you go with it?  It's like all those people hyphenating their surnames.

Possible.

definitely possible.  I already have dual citizenship and when I naturalise as a UK citizen in a few years, I'll be a triple citizen myself!

I'm pretty sure all Jews are entitled to apply for Israeli citizenship, so any Jewish person with dual US and UK citizenship could become an Israeli citizen as well if they wanted to.

My wife was born South African, then naturalized in the U.K.  She was going through the U.S. process when we moved to the U.K....so one day in the not too distant future triple citizenship is quite likely, though as I understand it both the U.S. and U.K. would frown upon it and discourage it.

Perfectly possible as long as you get citizenship of countries that allow more than one.  I know some countries make you give up your other citizenships to take on theirs. 

both the U.S. and U.K. would frown upon it and discourage it.

The US ignores other citizenships, the UK doesn't care.

Perfectly possible as long as you get citizenship of countries that allow more than one.

That's exactly it. My kids are Irish/British/American citizens.

How far could you go with it?

  Theoretically, I would imagine there isn't a limit, so long as all the countries involved don't require that you give up previous held citizenships.

Yes, as super says, the UK doesn't care.  The US officially ignores other Citizenships (though it can cause issues with security clearences and the like and do warn that taking on other Citizenships can cause conflicts which the US would not be readily able to resolve).  You also have to disclose to the US when you renew your passports that you have taken on another Citizenship but you didn't mean to relinquish your US one by doing so.

DS is a dual national, having been born in the UK to American mother, British father.  His girl friend was born in the US but her mother is Canadian and GF is about to seek Canadian citizenship.  Should they ever produce offspring, would that child be entitled to US/UK/Canadian citizenship? 

Depends on where the child is born. Canada's citizenship law will be changing by April, and in this instance, if the child is born outside Canada, it won't be eligible for citizenship.

But that's probably not what you were asking.

I was also born in the US to a Canadian mother and have recently submitted my Canadian citizenship application.

Interesting.

Depends on where the child is born. Canada's citizenship law will be changing by April, and in this instance, if the child is born outside Canada, it won't be eligible for citizenship.

Oh my! I am so glad this was mentioned because I am planning on submitting paperwork to claim Canadian citizenship for my 2 children born in the US but was waiting because I feel so burned out from all the recent visa paperwork I've been doing. I'd better get a move on with this!

I'm Canadian born, US and UK naturalized, so as others have stated... it is possible.

Oh my! I am so glad this was mentioned because I am planning on submitting paperwork to claim Canadian citizenship for my 2 children born in the US but was waiting because I feel so burned out from all the recent visa paperwork I've been doing. I'd better get a move on with this!

I'm Canadian born, US and UK naturalized, so as others have stated... it is possible.

If you're Canadian-born, your kids are fine! It's only the second generation born outside Canada that will be ineligible. So your grandchildren wouldn't get citizenship if they're not born in Canada. See http://www.cic.gc.ca/english/citizenship/rules-citizenship.asp for more details.

The paperwork is pretty straightforward, actually--the form is only 4 pages, and there's not a huge amount of supporting evidence required. And it's not that expensive. Depending on when you left Canada there might be some complications, but those should be fixed by the new law.

The US ignores other citizenships, the UK doesn't care.

They do, sorta, if you naturalize. There's a renounciation language in the pledge you take. However, the other countries of which you're citizen, presumably don't care what you tell the U.S. unless you tell it to them directly, and the U.S. follows the same policy as I understand it: you can claim alligience to another country and promise to foresake all others, so to speak, but unless you tell that to a U.S. representative, they don't really consider you having given up anything.

Or, I could have summarized the entire point above as /nit because for all practical purposes, U.S. ignores other citizenships and the U.K. doesn't care.