The New Testament as we have it today was compiled by the fourth century A.D. - NOT without heavy debate, I might add. But it was on the authority of the early Church fathers, and is more-or-less accepted as Biblical canon today.
But heed what Jaicee says, too; because the Bible was composed by MEN, NO ONE had any divine authority whatsoever to speak for Christ after he died.
As for adding or removing. The same as it did for ancient Israel (Judges 17:6, 21:25 - but read the entire book if you want to see this for yourself), everyone doing "what seems right in his eyes" results in chaos. If only for that reason, adding or removing is not an option.
But the reason that we have so many different denominations ("sects", or "factions," if you will), and no real Biblical standard, is because there are so many different interpretations of what the Bible says.
Here's an idea: Let's stop "interpreting" the Bible, and just let it say what it says. If we do that, we'll find that there is only ONE possible interpretation of it, and there will be no need to add or remove anything.