"step up further" is correct and usable in written English.
You might use it to describe someone taking an additional step in a process or situation. For example: "After completing the basic training course, the recruits stepped up further by taking the advanced course."
He was expected to step up further the security presence in the run-down suburb, as well as in those nearby, in an effort to stop the trouble spreading.
At one point, Klinsmann could be seen urging Kyle Beckerman to try and step up further into midfield to stop the attacking players from having to drop so deep to pick up the ball, but you could understand the RSL man's caution, as he anticipated having to shore up the back four as Honduras's wide men got between the midfield and defense.
In particular, the government of Bangladesh and other stakeholders could use our information to help step up further efforts to minimise mortality in that country.
Last year, Yonkers High fielded a junior varsity team and now it has stepped up to varsity -- stepped up further than planned.
After the Nice attack, Hollande said he would step up airstrikes further.
In fact, falling prices may prompt some companies to step up output further to maintain revenue.
With Jordan and Sam moving on it opens up opportunities for our young midfielders to step up and further their development".
Ms. Murray's willingness to step up only further cements her position as the most prominent woman in the Senate Democratic caucus.
"However, we know that this is only the first part of the process and over the next three months we must step up even further and rise to the challenge if we are to realise our full potential at London 2012".
And we have to step up for further commitments in 2030 and later years.
The results may not be easily replicated in the private sector, but they are likely to step up pressure by further undercutting the notion, prevalent at many hospitals not long ago, that infections are an unavoidable cost of doing business.
