Yes, people do this. But you might want to do 2 lifts harder (5’s + bbb > PR + fsl) and other two easier (5’s + fsl > PR). Going BBB with two lifts in same workout sucks.
Example:
D2 DL 5’s pro + 5x5 FSL
Press 5’s pro + 5x10 FSL
Week 1 Thursday
Bench 531 SS Chins
Press 5x10 @ 50% Tm SS Dbrows.
Week 2 is same, but alternate movements ( So Monday Dead 531, Squat 5x10 @ 50% etc)
Weeks 3 Monday
Squat 531
Deads 5x10 @ 60% Tm.
Week 3 Thursday
Bench 531 SS Chins
Press 5x10 @ 60% Tm SS Dbrows.
Week 4 same , but alternate movements ( So Monday Dead 531, Squat 5x10 @ 60% etc)
Week 5 and 6 same, but 5x10 work at 70%.
Overall cycle lasts 6 weeks, 7th week deload if necessary.
Once I ensured eating, sleeping, stretching and conditioning were given as much effort and consistency as the 2 days of lifting, this 6 week cycle gave me size, strength and confidence with the lifts. I will definately use similar 2 day programs as this in the near future.