N-Grams - how to predict further into the future and how far can we predict?

Question

I am using N-Grams to predict future character input. For n+1, it performs really well.

I've been looking, but I have not been able to find any information on what the feasible maximum distance into the future N-Grams are capable of.

One way I could do this is to predict the next character (n+1) and then use that result to predict n+2, use n+2 to predict n+3... etc... but obviously an incorrect prediction will cascade and impact the future predictions as there is a dependency.

Is there a better (more accurate, reliable) way to do this? Also, I can easily use N-Grams to predict the next (n+1) character in an incoming stream, but what about n+2? How about n+3? When does it become unrealistic to predict further?

I'm sure there is some research on this, so I'd love it if you could link me to a paper or give me a brief overview to get me going.