* Maybe couple dips with press instead of bench?
* Pullups right after deadlifts are gonna suck, they both hit grip and lats hard.
* Two days between 5x5 squats and intensity squats is pretty short.
What are your goals here? TM is often used as a peaking program for strength athletes. Your emphasis on press and addition of dips makes me think you maybe aren't prepping for a powerlifting meet.
If you are just trying to get stronger and look good naked (dips and chins baby!), I'm not sure a program designed around frequently testing your 3/2/1RM is ideal.
Maybe consider an HLM or 4-day HL split program? They are easier to fit some "bro work" into.
Example is my current split:
Su: H squat, L dead
Mo: H bench, chins, L press
Th: H dead, L squat
Fr: H press, chins, dips
Here, "heavy" is like TM "volume" and "light" is also volume, but not quite as heavy.
This is no good for peaking, because there's no day where you set rep maxes. You stop all sets 1-2 reps short of failure and trust that your maxes are going up. I.e. it's an "accumulation" or "hypertrophy" program. Which is my goal.