Volume. Usually it's attained by doing 5-7 sets, even 8 in some cases. Reps can be in the 6-20+ range. For example, I like to pyramid up and back down again for chest presses (dumb bell or barbell). 4-5 sets for accessory work. Superset, and the like are wonderful to. I use that principal for most muscle groups. Then, as Razor pointed out, frequency of training muscle groups factors into volume over time. You want to train a group to the point such that they are recovered by the next training session that you intend to target the muscle group again, 3-4 days. That's called maximum recoverable volume. Mike Israetel spells the theory out in great detail if ur interested. Google like Israetel MRV.
So, it high volume and increased training frequency that really could result in hypertrophy for you. It takes consistency over an appreciable amount of time. However, having been into powerlifting, you have the advantage of neural drive. Change the approach and you might just be surprised with your results
If i get a chance I might post up an example of a micro cycle training program (10+ days).