My understanding is to cross someone is to just be a dick to them. To double cross them is to be nice to them, then to screw them over.
So what is a triple cross? Is that where you pretend to be nice, then screw them over, then pretend to be either their savior or ignorant?
Example, I was reading Edward Snowden’s bio on wikipedia, he mentioned how the CIA set up a banker in Europe. The CIA encouraged him to get drunk, and encouraged him to drive home. When he got arrested, the CIA intervened and got him off. So they screwed him over, then offered to save him. Basically a leninist strategy, create a problem then offer the solution.
I would think it would be the opposite because if you “cross” someone in any form, you have to be bad to them in the end.
So if you were mean to them, and then pretended to be a double agent that can turn the tables on them, but you were really working for the other side the whole time, that would be a triple cross in my book.
I doubt that it has a precise meaning. Presumably it is meant to be be something like double crossing, only more so.
Incidentally, I do not think your your definition of double crossing is very good. To double cross someone is to give someone reason to trust you over some matter, then to betray that trust. I suppose if you got someone to trust you, appeared to betray them, and then turned out to be acting in their best interest all along, that might reasonably count as a triple cross, but I doubt both whether that often happens, or whether the term “triple cross” is regularly applied to it when it does.
Say I am close friends with Edward Snowden, and know where he is. I approach the CIA and offer to rat him out for a million bucks, thus double-crossing Snowden. I then offer to sell the info on where the CIA is picking up Snowden to TMZ so they can film it an embarrass everyone, thus triple-crossing the CIA.