There are two ways to do this. The first way is to add in “big” assistance work such as SLDL, Deficit Deadlifts, Front Squats, Rack Pulls, SS Bar Squats (or any big movement). You can use 5′s Progression or SST with any of these movements. When you add in the big assistance work, I’d start by dialing back your training maxes of your main lift to at least 90% of your max and don’t go for max reps. Just keep things ”even” with your heavy lifting. Don’t push everything that hard – keep the intensity up, but the volume LOW. Remember that in training and in life, there’s a balance to everything – a push and a pull. You push something into your training and something has to come out. In your case, you want to push up the volume of your assistance work to elicit greater gains in hypertrophy. Because of this you have to pull something out.
The second way to increase assistance work is to use small assistance work that is easy to recover from – in other words exercises such as dumbbell raises, lat movements, machine work and single joint exercises. These exercises are not tracked for weight or records. Rather these movements are done with one goal in mind; to get a big pump. If you choose to this route, there is no need to adjust your TM as these movements and the way they are done should in NO way effect your main training. If they do, you are doing something wrong.
The problem with the increase in assistance work is that everyone wants to have their cake and eat it too. It doesn’t work like that – you can’t be strong like a powerlifter, fast as sprinter, and as big as a linebacker. Well, you can, but these people are so rare that teams pay them millions of dollars and television stations have billion dollar contracts to broadcast them to you. They’re called professional football players, and if you’re one of them, you aren’t reading this, as you’re too busy counting your money and cracking skulls.
So if you want to increase the volume of your assistance work, follow the plans above and use your head. Also, less typing – more training and eating.