"move a step further" is correct and usable in written English.
You can use it to describe taking a course of action that is an advancement over a previous one. For example: "We have achieved success with our recent project, but now we need to move a step further and plan for the future."
Wednesday's iPhones 6S launch event saw the company move a step further, putting three women on stage: Jen Folse, a senior design producer at the company who introduced the new Apple TV; and two guests, Michelle Peluso, who introduced her company Gilt's Apple TV app, and Irene Walsh, head of design at 3D4Medical, who demoed an iPad Pro edition of its medical app.
In this paper, the authors move a step further towards the identification of impacts for realistic tube vibrations.
To move a step further, this paper introduces a parameter control approach that utilizes such measures as feedback to adaptively control evolution processes.
When we move a step further down from theory, we observe that description itself is an abstraction of, or rather, a generalization from the analysis of particular text instances in language (see Fig. 2) – and, in the context of typology, a generalisation from descriptions of various languages.
Finally, an interesting and important discussion issue is whether our goal is to provide comprehensive guidelines for small-animal PET and SPECT imaging, or whether it is worthwhile to move a step further, and work on an accreditation programme of scanners and procedure along the lines of, for instance, the accreditation for human FDG-PET as set up by EARL (see http://earl.eanm.org).org
However, once the patient's status is categorized as metastatic, the diagnostic work-up has to move a step further.
Stansted, Hong Kong's Chek Lap Kok and now Beijing have each moved a step further in perfecting lightweight structures.
Now he is moving a step further -- to m-commerce -- and he has come to First Tuesday to spread the gospel.
This week, the phenomenon seems to have moved a step further down the line into old-fashioned B-movie madness after Hollywood studio Warner Bros and production company Legendary confirmed a release date for King Kong v Godzilla movie for 2020.
Updated, 8 55 p.m. | LONDON — American and British authorities moved a step further on Wednesday in their investigation into the manipulation of the benchmark interest rate known as Libor, fining the British financial firm ICAP a combined $87 million for its role.
Southport moved a step further away from the drop zone with a comfortable win over relegation-threatened Dartford.
