Definitely add in some core work, both weighted and bodyweight (I personally find hanging leg raises from the chinup bar to work both grip and core strength).
If he really wants some arm work, adding it in after his deadlift day would be a good place to put it, especially if he is going to remove that chest accessory. 2 days rest seems like it would be really nice for this routine.
I also don't know what his endurance is like, but getting some GPP in as well would be nice.
Class I Total @ 198: 525/335/600 (1460)
"No citizen has the right to be an amateur in the matter of physical training.... What a disgrace it is for a man to grow old without ever seeing the beauty and strength of which his body is capable."