"no further objections" is correct and can be used in written English.
It is used to indicate that no one has any objections to something. For example: The team presented their plan for the new project, and when no further objections were voiced, the meeting moved on.
With no further objections lodged, the company was dissolved on 29 September.
The LV process was finalized at the point at which no further objections from either the translation company representatives or the pharmaceutical industry representatives were raised.
After the final argument for immortality (102a 107b), Cebes admits that he has no further objections to, nor doubts about, Socrates' arguments.
I for one have no further objections to this data being handed over from a privacy standpoint, although I still urge Viacom to stop the endless litigation and consider more innovative business models around their content.
With that amendment, the Production Code Administration had no further objection to Rhett's closing line.
Before he could voice any further objections — the dust, the fumes — she had spotted a pair of overalls hanging on the back door, and the next thing he knew she had scrambled into them and was demonstrating how well they fit; her belly split the front like a chestnut its shell.
It lay there unopened on the parlor table while I thought of further objections.
The Senate could have further objections to Trump loyalists, Galen believes.
Further objections came today from Egypt, long a close ally of the United States.
Further objections from South African unions and others will be heard by the Competition Tribunal, another official body, next month.
Three months ago, after further objections in the US, but before our investigation, Secure Flight was suspended after costing the US taxpayer $144m.
