"further antagonize" is a correct and usable phrase in written English.
You can use it when you want to describe a situation where someone or something has increased or will increase negative feelings. For example, "His refusal to apologize for his behavior further antagonized his peers."
Do we further antagonize Muslim populations who already deeply resent our policies in the Middle East?
Many were in favor, but Goodwin, who had the longest tenure and remembered the 1985 strike vividly, was unwilling to further antagonize the pilots.
Juggalo Gathering LLC added that the performer exacerbated the situation when she "removed her top, exposing herself, which seemed to mock and further antagonize the crowd".
And Russia, like China, appears in no hurry to take action that, in its view, would only further antagonize North Korea and destabilize the Korean Peninsula.
Iraqi diplomats said they were worried that after the Turkish prime minister, Recep Tayyip Erdogan, met with President Bush on Nov. 5, Turkey may take action against the Kurdish guerrillas, a step that could further antagonize Iraq's Kurds.
Administration officials were divided over the sanctions, with some voicing concerns that they would further antagonize Arabs alarmed by the American handling of Iraqi prisoners or the administration's support for ceding parts of the West Bank to Israel.
He further antagonizes people in the education world.
Mr. Khatami's aides have said they want to move slowly to avoid further antagonizing conservatives.
Mr. Mashaei finally withdrew on Friday, but the president renamed him chief of staff, further antagonizing hard-liners.
Assad further antagonized the opposition with a media interview that indicated he has every intention of remaining in power.
These fears seemed to drive them to grab more power, as a way of protecting themselves, but every step only further antagonized their enemies.
