Hi fellow strength enthusiast, my quest pertains to the types of assistance exercises that are wise to do on the same day as the parent movements. In Practical Programming 3rd addition Rip talks about how movements like rack pulls and presses are better used as short term replacements then added in with parent movements. The reason being that these movements would be considered overloading movements allowing more weight to be used due to shorter ROM and therefore too stressful to do on the same day. On this same logic would it be ok to use a movement like box squats or rack bench presses if it's done with a weight that allows for say 10 reps? This is basically the concept with 5/3/1 and the " big but boring" template, where the parent exercise is simply repeated with a reduced load for 5x10.
As Adam said, it's impossible to talk about programming without knowing you and your training.
In general though, from personal experience in the early advanced range, introducing low-intensity high-volume assistance work to fix a particular weak point can be done without much planning. For example, I recently introduced an additional day of 3x8 presses once a week at roughly 75%.
On the other hand high-intensity work or light-but-difficult version of the lifts (paused squats, box squats, etc) must be introduced very slowly to not affect recovery. It can be difficult to know when you are digging a recovery hole for yourself, and difficult assistance work on top of an already difficult program is an easy way to break ground.
For an intermediate lifter on the four day Texas method who whilst loves powerlifting, have ties in bodybuiling. And a few of my accessory exercises reflect this. Rear delt FB flies due to underdeveloped rear celts, and standard BB curls. Other than those two exercises though, all my other lifts are there to support the main movments.
The reason why I ask this is because I didn't know whether it would be better to use a rack bench on volume day instead of the standard bench because that's my weakest lift, and I seem to always get stuck about 1/4 of the way up. Or if I should just use rack presses as a lighter assistance exercise done after my bench and military press.
Assuming you're around intermediate, weak point analysis isn't useful -- that's just you discovering where bench is difficult. Don't train to address a specific point on the bench; just get stronger through the whole movement. For example, if you were faster out of the bottom by virtue of being stronger, the sticking point would be easier.
That said, something like rack presses would be best done as assistance work. You probably don't actually want to do rack presses as they will cause you to be out of position -- what about pausing a light bench at that point for a 2-count?
Are you already using the TM or is this evaluation based on your LP performance?
If it is the later then maybe the increase in volume will fix it.
Are you stalling on BOTH volume day and intensity day?
The guys at 70's big would often keep the weights on volume day the same UNTIL intensity day stalls, which is to say don't worry about it if you cannot increase the weights on volume day every week as long as intensity day keeps moving up..
If I were to incorporate rack presses into a TM routine, it would be as the main exercise on ID for a few weeks. I've done them as a max effort exercise in a westside-based routine and they work very well, but not necessarily as a long term thing. Cycle them in and out.