I am doing one for a competition -I hopped it like a double or Imperial IPA in the boil, but I am hopping it with three dry hop additions added in separate increments.
Triple IPA is more marketing buzz than actual style. You could characterize it as anything on the extreme high end of the alcohol scale (>10% ABV) for Imperial IPA. Pliny the Younger would be the prototypical version of this.
The trick is to make sure you are still in IPA territory and not barley wine. To ensure this you need to use a large amount of simple sugars -- or "White Malt" as Vinnie calls it. And then just hop the hell out of it. If you ever ask yourself "Is there too much hops in this?" the answer is NO.
Double IPA gets its name either because there are two I's (IIPA), for imperial IPA, or just double because of having roughly double the alcohol.
For what you describe, I would call it a Triple Dry Hops Brewed Beer.
What was your reasoning for putting the dry hops in at different intervals, and which hops did you use?