I’m running this setup right now: https://www.t-nation.com/training/complete-power-look-program
On bench and push press days, I superset the two assistant lifts with a pull. Usually one that hits upper back (face pulls, elbows-out rows, etc.) and one more lat targeted (pullups, rows, etc.). In addition, I make sure one of my assistant lifts to deadlift is a pull typically targeting the traps like a kirk shrug, or snatch high pull from hang.
Because the goal is the 4 main lifts and the specific work for them is pretty intensive, I’m not taking any of the sets for back to failure or anything and usually sticking to the 8-15 rep range. I’m really focused on effective muscle activation and just getting the work in. This approach has not negatively affected my performance on pressing movements at all. If anything, it helps, as I feel more stable and mentally amped up from a faster paced workout.
If back is really a weak point, consider adding a 5th accessory workout focused on back and bis. I haven’t felt that was needed though honestly.