The phrase "further consolidated" is correct and commonly used in written English.
It is typically used to describe something that has been strengthened or solidified even more. Here is an example: "The company's position as a leader in the industry was further consolidated with the acquisition of two major competitors."
Republicans further consolidated power in 2012 with the election of Mr. McCrory.
Finally, in 1684 Charles further consolidated his position by defying the Triennial Act.
The move further consolidated Mr. Giuliani's political control over the seven-member board.
Then there would be a second phase, in which the trust between the parties would somehow be further consolidated.
Kosminsky's reputation as a director who heads to the hottest part of the battlefield is likely to be further consolidated.
Pigmeat Markham and Sleepy LaBeef, who were among the earliest singers to adopt meat-themed monikers, further consolidated the alliance between meat and music.
These were further consolidated in 1970 71 into even larger groupings, called agro-industrial complexes, that took advantage of integrated systems of automation, supply, and marketing.
A broader Croatian ethnic identity would be further consolidated among the Catholics of Dalmatia and of Bosnia and Herzegovina during the nationalist movements of the 19th century.
This decoupling was further consolidated in the Germanic period (i.e., Visigothic and Sueve domination of the region), with a sharp decrease in mining/metallurgy but continued grazing.
Another progradation dynamic during the Little Ice Age, at a time of strong rural population growth, river discharge increases, technological developments, and urbanisation, further consolidated delta growth.
Electrodeposition was used to successfully fabricate MWCNTs/Cu composite powders which were further consolidated by hot pressing followed by cold rolling.
