Do your chin up sets of 10 between pressing sets on bench and military press.
Then do some barbell rows SS with your other accessory movements. The chins won't kill your pressing (may actually help), and the rows will become your lead accessory movement. You'll increase your volume without overturning the apple cart entirely. This is in 5/3/1.
I hate barbell rows. They seem to be too tiring on the lower back on top of squats and deadlifts. DB or Kroc rows are better, as well as any kind of weighted/BW pullup or chinup. Another option would be cable pulldowns or face pulls. Just add 3-4 sets after every session and you should be fine.
Face pulls or inverted rows are the gods of upper back development and shoulder health. They lean towards the high volume end of the spectrum, sort of. You are a man with notable traps if you can do 20 inverted rows with no rest.
Doing sets of face pulls at the end of every workout has helped me out a great deal. I also try to do a few sets band pull-apart variations every day -- nothing crazy intense, but good volume, especially for the stabilizing muscles in the back.
What I do if it helps; sets of facepulls between sets of bench (mon) sets of pullups between sets of military (thur) sets of Tbar, or DB rows, after deadlift work, 3-5 sets, (Fri) On a BBB template that gives you around 25 sets for back a week, plus your deads, and squats. 2cents
Do it do it do it do it!!! Once a week. But don't stop rowing 2-3 times a week. Snatch grip pulls are awesome but work the upper back musculature in a bit of a static way (though you COULD count sweeping the bar as a mini lat contraction); your thoracic erectors will get thick, and lifts that depend on that will skyrocket (so most lifts), but nothing beats actively contracting a muscle through a dynamic range, if for only the central nervous system education. Rows rows rows rows. Chest supported/ facepulls after benching, strict and awkward power hump bent over rows after deadlifts, I'd suggest pendlay, but whatever, I've written too much as it is.
75% of my upper back work is with inverted rows now. One workout I put my feet on a 12" box, and use 3 different rack positions, about 30, 33 and 36 inches off the ground for the grip. This makes the pull to the low to high stomach area. The second time I will have feet on the floor again with 30-36 inch high rack position which puts the pull point to the lower chest, mid chest, or clavicle area. Also will use a weighted vest.
Inverted rows with BLAST straps are the tits. infinite row angles, endless wrist position possibilities and you can row past where you can with a barbell.
If you don't have blast straps, make some with a couple "D" rings and a length of small chain for each handle and a couple carabiners to hook the d-rings to the chain. Then hook it to a power rack, the ceiling via a eye bolt into a rafter etc.
Just to echo what mertdawg and StrengthDawg were saying, suspension trainers in general are great for low intensity, high volume/frequency upper back training. Inverted row variations, scarecrows/reverse flyes, face pulls, external rotations, YTWA series, etc.
Two things I guess, #1 I'm with everyone on suspension training, I have a home made set up with anchor's in the wall, and ceiling, Than I bought 3 different length tow straps 4ft,6ft,8ft (auto-parts store $10) with hoops stitched in each end, and other than Tbar rows (tow strap for this too) I do all my face pulls, and rows suspension style. I do my face pulls against the wall, with anchor at face level, and 4ft strap, just leaning back with feet jambed against bottom of wall, hundreds of these.
#2 Op wanted to know about high pulls, I've been doing them about 3mths now, since CT's article like everyone else. I was already doing cleans on squat day, 5 sets before I squat, So I added in high pulls on Dead day, I do 3 sets before deads, on the way up, and 3 sets after deads on the way back down, I do them hanging, and it works out well this way. Once I get stronger at them (above 250) but right now it works fine. here's a week to give idea
Mon. Bench (531-10sets) supersetted with facepulls (against wall) 100 side latterals (finisher) Tues. Cleans, 5 sets, - Squat (531-10sets) supersetted with core work, 100 BB curls ( finisher) Thurs. Military (531-10sets) supersetted with pullups, 100 front,or rear latterals (finisher) Fri. Deads (531-10sets) high pulls worked in to my ramp up, and back off sets, finish with Tbar rows 3-5 sets of 10
This has been working really well for me, I have been following this since Jan, Preparing for a meet after a long layoff, and i'm getting bigger, and stronger by the week. The most noticable thing from this routine are my traps. they've doubled in 6 mths. goodluck
I like high pulls in general. I can do them from about 4-5 different rack heights, and a clean, snatch or in-between grip, and I will put bungees across the power rack somewhere between about 42-54 inches to create a target height. Then I will often attack some bands to the bar as well. Pulling to 42 or 45 inches is quite low, and really a power shrug. These never cause me problems like UR rows, and they actually seem to keep my shoulders feeling good.
One exercise that helped me out a while ago was Cuban raises, done rather strictly for feel. Actualy because my internal rotators are already providing resistance, they didn't need to be that heavy. I would do 100 Cubans alternating arms with 10-15 pounds. My shoulders never felt better, and it did correspond to my PR in the bench. I like them better than face pulls.
Anyway, clean pulls accomplish much the same thing. The problem with them is that I use metal plates so I don't drop the weight, and it turns into a lower back exercise. I got a couple minor leg pulls when I squatted after clean pulls, and got some back soreness from the "catching" at the bottom, though the bands tended to keep the weight from drifting out too much. Also setting the bottom rack position higher will reduce the weight and put it more on the traps.
Also I don't want to add another back exercise into my squat workout these days (one squat, one goodmorning, Zercher or dead-pull variation), and I don't really want to add vertical loading on the spine on a non-squat day. I know though that Metal Militia and or Nazbar guys do lots of heavy power type shrugs once a week for the bench press. I hate smooth, strict shrugs though. I would prefer shrug carries, or power shrugs with some arm bend. Also a shrug can be more of a rounded back internally rotating type of move, while a pull has the scapula tilting back rather than rounding forward (which I think is good for the shoulders).
The reason I just went ahead, and showed my weely workout schedual was to show how back gets hit. I have BBer friends that can't believe I don't have an official back day, where I ruin my back. If you look at my 4 day break down, I hit back every time I'm in the gym (same with most PLer's I think) My back is the secondary muscle group(exercise)of the day suspersetted or after main lift. This means the back exercise dosen't get the intensity of the main exercise, therefore the volume, and somtimes the reps are much more (I aim for double) I can't speak for other's but my back thrives on this, strangely my back is what most people comment/ask about the most. Anyway OP your right it was Dallas that brought up high Pulls, as far as rack pulls, and snatch grip. I always heard that doing snatch grip deads for awhile adds all this muscle to your back (rack pulls would be the same) it's never done anything for me personaly. I think this is because I dead lift wide to begin with, fingers on outer ring, so it might be effective for narrow people, lots of big names swear by it.
What I do know that as a PLer that likes to look like a BBer, adding in cleans earlier this year, and high pulls has done freaky things to my back, and traps. if somone told me that I could change my back this much in 3mths, I would have thought it was bull shyt. It's also helped my lifts, and I'm not running any gear right now. I know I sound like a sales man, but in 20yrs of lifting I've never had a growth spurt like I've had from adding in these two Oly lifts, wish I had before, and after pics.
OP we've gotten off original question, but what I would do is put face pulls in instead of chins on one of your upper body days, Than add some heavy pulls at the end of each lower body day, snatch grip from the knee, would be fine for one. the other day try one of the OLYs 5x5 or a heavy bent or Tbar row, 3x10-15. Don't kill yourself leave a coulple reps in the tank on each set, just put the work in, give it a couple more cycles, and your back should come alive. Remember paitance is power, in more ways than one!