The phrase "a further compromise" is correct and usable in written English.
It can be used when discussing an additional agreement or concession made in a negotiation or discussion.
Example: "After much deliberation, the parties reached a further compromise that satisfied both sides."
Alternatives: "an additional concession" or "a subsequent agreement".
We then worked on a further compromise.
A further compromise on slavery prohibited Congress from banning the importation of slaves until 1808 (Article I, Section 9).
The Bush administration's abridgment of privacy protections for medical records (front page, Aug. 10) reflects a further compromise of societal concerns with privacy.
As a further compromise, the bill will permit the sale of other fishing tackle, like jig-head lures, that may contain lead.
As the bill moves to the Senate, lobbyists say they are focusing on a handful of Democrats -- including Robert Menendez of New Jersey, Maria Cantwell of Washington and the chairman of the budget committee, Kent Conrad of North Dakota -- to reach a further compromise that would lessen the sting of the change.
We speculate that the initiation of the medical therapy led to a further compromise of the optic nerve function consequent to the overwhelming inflammatory reaction that sequentially settled following the use of high-dose steroid therapy.
As a measure of any further compromise in DNA replication efficiency, we examined whether the G2/M transition was additionally delayed in orc2-1 hat1Δ strains using flow cytometry.
Since you started with a compromise, further compromise is not acceptible.
But loading the atmosphere with CO2 from burning fossil fuels isn't so much giving "food for plants", but rather a way to further compromise the food supply of the world's poorest people.
The disruption of potential hydrogen bonding interactions by substitution of a hydroxyl group with a fluorine further compromises these substrate analogues.
Since infection is a leading cause of death for SLE patients [50], it is possible that a prolonged state of reduced responsiveness to IFNα may further compromise a patient's ability to fight infection.
