i bet you could if you trained them every day, religiously. Another option is to have them go 5 feet up and then string them at a 45 degree angle to another 10 foot post a distance away, you could easily get 20 feet that way. I built a giant cross that is 23 feet high, I do believe my neighbors are living in fear.
I've been trying to think up how to set mine up too. Space is an issue. I have an 8' section of fencing along the side of my yard to work with.
My wife (the gardener of the two of us) drew up plans that might work. Attaching 10' posts to the existing fence posts that will give us 13' of height. Running 45# picture-hanging wire between the two. Then running a 4 rows of twine up and over.
She signed it Wiley Coyote, Supergenius.
Love that woman.
A little bit of math will tell you how much more length your angled twine will get you vs. going straight up. In my case, it was only a third of a foot or so, but my hops are only 3ft from the base of the pole. My post is about 13' and the Chinook will just have to wave in the wind
10' is fine.. My trellis is 12' tall, it looks gigantic in a suburban neighborhood with a 6' limit on fence height. I'm confident I'll get a decent yield, maybe not as great as the 15'-20' guys, but whatever - I have 9 plants, it'll be fine.
This year I put a 4*4 post in the ground that is LOWER than my 6' fence. These are permanent. I bolt two 2*4's to the sides of this post with a block in the top. This allows me to have a tall trellis in season and nothing (seen over my fence) out of season.
I recently finished up a trellis as eye sore issue thread. My trellis last year was pvc (thin) and 10' tall. This year it was 8" thick and 8' tall and I got vetoed. The solution, free beer to my neighbors and they got over it. I tweaked the design and now will telescope (hopefully) to 11' or 12'.
If you google it, I know I've seen studies of professionals using 10' designs rather than 20' designs. I thought I read they nearly as effective in yield terms and lowered labor costs. Even though I'm on the "as tall as you can" team, I think there may be something to these 10' trellis systems.