"pushes for" is a correct and usable phrase in written English.
It is used to express a desire to obtain or achieve something. For example, "The mayor is pushing for stricter regulations on waste disposal."
Citizens UK pushes for change.
It also pushes for Security Council attention.
In court, the industry pushes for letting the E.P.A. regulate.
It pushes for a lower corporate tax rate.
But Sachtleben won't budge and eventually pushes for charges against Lenz's killers.
He pushes for the curbs on healthcare and entitlement spending that his own party has resisted.
His version pushes for the elimination of "unfair tax breaks for millionaires".
The attacks on the United States, which still pushes for Iran's isolation, were sharp enough.
Then Stokes pulls hard for a couple, and from the last he pushes for a single.
"To the degree he pushes for anything, it's behind the scenes.
October 18 , 201210.07pm BST David Cameron pushes for banking supervision Pointed remarks.
