The phrase "but also further" is correct and can be used in written English.
It is often used to introduce a contrasting or additional idea or action. Example: "I was impressed by his excellent communication skills, but also further impressed by his ability to problem-solve under pressure."
"The parliamentary functions must be not only strengthened, but also further extended".
Then chin-ups, piano, further maths – as in more maths but also further maths as in more advanced maths.
The findings not only undermined the government's case but also further eroded the credibility of the nation's criminal justice system.
Students will examine food production from the early cave dwellers right up to the nineteenth century - mostly in the 'old world', but also further afield.
First steps, and smiles, and days of school all bring our children closer to something — but also further away from us.
Mr. de la Fuente succeeded in turning up the pressure on the strikers to settle, but also further polarized the conflict at the National Autonomous University of Mexico, a conflict that has moved to the center of Mexico's political agenda.
Ukrainian forces are struggling hard to seal the porous border with Russia, not just near Dmytrivka but also further north at crossings that have been the scenes of fierce battles.
If a high number of civilian casualties is confirmed, it is likely to not only deepen antipathy toward NATO forces in Afghanistan, but also further diminish support for the war in Germany, where it is already unpopular.
It not only avoids the downside risk, but also further explores the upside profit successfully.
Compared to DNN7LS, DNN8 further improves CD, LLR, and SNR, but also further degardes the SRMR.
But also: further evidence of how totally Assange seems to have lost its grip on reality".
