"further persuade" is correct and usable in written English.
You can use it when you want to talk about convincing someone to do something in an additional or stronger way than before. For example: "I will do my best to further persuade my boss to approve the budget for the new project."
A lone police car is cruising around but no one seems to be trying to further persuade residents to leave.
One man who did find the back of the net was 33-year-old defender Wes Brown, who marked his return from more than a year on the sidelines with his side's second goal to confirm his fitness and further persuade manager Paolo Di Canio that he has a part to play next season.
In a June 1 letter to the U.N. Security Council, Deng Gai sought to discredit the presence of Machar's people and further persuade the U.N., the African Union, and IGAD "to desist from engagement" with the rebel leader.
Perhaps, despite my objections, the success of films like: The Help, Django, The Butler, or 12 Years a Slave, will further persuade Hollywood to widen its view and edit its erroneous perception of what a commercial black film can look like.
This question of "why didn't you leave?" can further persuade survivors to seek the false comfort of the abusive relationship because they would rather stay than speak out and risk being shamed, stigmatized, judged, questioned by the very people who are supposed to care about them – friends, family, and even the criminal justice system.
I needed no further persuading.
He may have kept repeating the injunction to enjoy, but almost from the start, his audience needed no further persuading.
I was further persuaded into this madness by a younger friend whose money and dignity were not at stake.
They were guaranteed by bond insurers, like Ambac, further persuading people there was nothing to worry about.
A review of the bid histories of a half-dozen eBay auctions of similar electric clocks during the past month further persuaded me.
Bloomberg's huge advertising budget and his reputation as a moderate further persuaded independents and some Democratic voters to abandon Mark Green, the Democratic candidate, whom he outspent by five to one.
