The phrase "after some further" is correct and usable in written English.
It can be used when indicating that additional information or clarification is needed after a previous discussion or point.
Example: "After some further consideration, we decided to change our approach to the project."
Alternatives: "after additional" or "after more".
After some further unpleasantness, God destroys Sodom.
After some further analysis, Econoval managers concluded that the strategic plan was financially feasible.
(After some further modifications, it eventually flew for 500 metres [1,640 feet] in 40 seconds).
The witness was then recalled and, after some further examination, three of the remaining reports were put in evidence.
After some further hemming and hawing, I offered $4,000, the upper reaches of what I was willing to spend (and even then I'd sleep guiltily).
After some further questioning, the judge dismissed a man who said he "would have some explaining to do" because his father was a retired police officer.
Eventually, after receiving some further guarantees for his country, Czech Pres.
To finesse this further they looked at letters written by Monet during his trip to the area, and after picking out some further clues (the painter was particularly careful in his observations of the tides) they arrived at a final time and date: 5 February, 1883, 16:53pm.
I feel that after Tuesday and some further legislation I will be paying socialist levels already, though that is neither here nor there.
Although these two factors (education and fertility) must certainly play an important role, as we have shown above, even when we condition on education and children, there has been a significant increase in female employment after 1990s.There is some further evidence that child bearing is an important determinant of female labor force participation.
On Feb. 9, after I sent the revised version to my colleague, he suggested some revisions in accordance with provisions of the Constitution; after that we made some further slight changes in wording based on feedback from other media organizations.
