This is the position of the Mormons and the Ba'hai, but not of Nicene Christianity.
The problem is that there is no authority to "open the canon." The traditional marks of christianity (See What are the biblical arguments that the Bible canon is closed? and https://christianity.stackexchange.com/a/11442/1039 ) are apostolic authorship and historical consensus. As all the apostles are, in fact dead, there is no means for using this mark.
Beyond that, it is taken as an article of faith by most Christians that God never changes. By opening up the canon, too many cans of worms get open.
This is not to say the prophetic word doesn't continue to be uttered, but they exist within the realm of revelation which is assumed to be complete at this time.
Finally, there is one more point to consider - the church is long since past the place where it can definitively speak with one voice on something as large as a whole new addition to Scripture. I would point you to the last paragraph on this question about canonization in which I wrote this:
Even today, there are certain Christian authors who are considered "more important" than others. If you asked me to pontificate about who is canonical, for example, I'd want to throw in C.S. Lewis, G.K. Chesteron, Augustine, and a couple of others. David Barton, Joel Osteen, Tim Lahaye, not so much. And, I would clearly reject, say, (and I only speak for myself) anything by Joseph Smith or the Watchtower society. Why do I say that? Because my canon speaks to what is important to me. Many Evangelicals would probably agree with me, and do, as can be shown by what other Evangelicals tell others "should be read." The point is not what I've picked, but rather that the same process was in place 2000 - 1600 years ago.
As a Christian, if you read anything other than the Bible, you are picking your canon. Whether or not others agree with you is up to them. I recommend The Great Divorce a lot. As such, I'm making my own canon. Indeed, many people would probably agree with me on it - but not the whole church. And that is the problem you'd have to contend with if you wanted to reopen a "Newer" Testament.