If you are trying to add a lot of
pure chest strength (instead of stabilizing muscles and core) then you should try weight vest push ups.
The function of your pecs is to draw your arms across the chest, and this is the exact same movement that makes up dumbbell flies, which is why this move is noted for helping build real,
functional chest strength.
Now I claim that this down and back position increases
your chest strength, why?
Well talk about how it increases
your chest strength increase in a bit but lets first talk about shoulder safety.
THIS is what's going to make you be able to lift 10 to 20 % more weight... it's not that
your chest strength has increased... it's just that you're now able to generate leg drive and stabilize your core better.