Very rarely do I program more than five reps of of a main lift for an athlete. Why? For beginners: it helps keep technique in check and helps them to stay focused (I often see the young athlete's eyes glaze over and head turn left+right to look at other distractions once he or she passes the 5-rep mark!).

For the intermediate and advanced lifters: low reps keep recovery prompt and hold muscle soreness at bay. Having an athlete perform sets of ten to twenty on the squat would leave him/her absolutely torched come game day or time for sport-specific technique work.

Not to mention, sets of four to five reps seem to be the crossroad for muscle building and neural training. You can still pack on some size, while at the same time teaching the neuromuscular system to contract faster and with greater force.

Anyway, higher reps can still have their place in training, especially for the "Joe's and Jane's" out there simply looking to pack on some lean body mass. I have also found that some athletes respond better to higher reps, but I still want to keep the total volume in check. So, how does one go about this? How do you simultaneously train strength and size, without adding too much volume that it becomes detrimental to the nervous system?

First and foremost, be honest with yourself. If you're still a beginner (can you realistically squat 1.5x your bodyweight with perfect form yet?), and even if you've just entered into the "intermediate" portion of the continuum, don't even concern yourself with this strategy. In all likelihood your technique is going to breakdown and you'll expose yourself to injury.

Moving on, here's what to do if you're at the appropriate stage in your training:

Do a few heavy sets, and follow it up with one "back off" set of higher reps.

This way, you stimulate the high-threshold motor units via lower reps, and provide a solid strength stimulus. Then, the bodybuilder side of you can satisfy his/her craving via the "get your pump on" set at the end!

Here are a few examples:

3x5, 1x10 3x4, 1x12 2x5, 1xAMAP ("as many as possible") 3x3, 1xL2ITT ("leave two in the tank")

There are a bunch of ways to do this really. Putting the last example into a real-life example, here's something I might do....

Using chinups as the lift of choice, I may work up to a heavy set of three, but still ensuring the reps are crisp and I'm not grinding them out. So, I might work up to 110x3:

Rest a couple minutes, and then do a bodyweight set of 17-18 chins, leaving a couple in the tank (it should be obvious but just in case: that higher rep set should utilize much less weight than the heavy sets).

I find these set-rep schemes lend themselves particular well to chins, squats, pushups, and rows.

A couple caveats:

Don't do this year round, but cycle in a few, 3-4 week blocks of this throughout your yearly training
Be especially careful with the squats, stopping the set if you're near failure and/or are turning your squats into an ugly "goodmorning/squat" combo. The more squat videos I see on the internet, the more hesitant I become in providing public advice like this because most people's technique is atrocious at best.
I'd avoid this high rep back-off set strategy with deadlifts as the risk:reward ratio simply isn't worth it.

That's it. You can use your imagination really....just do a few heavy sets, staying away from failure, and then back off the weight and get your pump on with one, higher rep set to finish it off.