'further draw' is correct and can be used in written English.
It can be used when you want to emphasize a connection between two topics. For example: "The similarities in the two pieces of artwork further draw attention to the artist's eye for detail."
Did that further draw him to the story?
I used the text to further draw attention.
Like BT, Sky is hoping to further draw together internet and TV services, and from September will start offering a Wi-Fi capable Sky+HD box as standard, as well as new wireless adaptors to upgrade older hardware.
The anti-euro AfD – Alternative for Germany – has been gaining political support since the European elections last May, and is now trying to use the anti-Islam Pegida protests in some parts of the country to further draw disaffected citizens into its orbit.
They were also part of an effort to further draw attention to the alliance of Hezbollah and Iran, which American and Israeli intelligence officials have sought to portray as a subversive collaboration that has not only destabilized the Middle East but has been implicated in terrorist violence elsewhere, including a deadly bus bombing of Israeli tourists in Bulgaria last month.
Oh, and while you're here, buy some video games for your children!" So, Amazon gets more exposure, and Best Buy gets a hit product to sit on its shelves to further draw customers.
Andrea Bowers goes further, drawing select figures from photographs of activist groups practicing nonviolent resistance.
Mayor Dean goes further, drawing on the age-old traditions of American civic boosterism.
Moreover, the well-intentioned humanistic focus on the individuality of the victims further draws attention away from the horror.
The daily Le Monde went further, drawing parallels between this "strange defeat" and another, on the front lines of 1940.
"She started the faux-old movement that I want kids to take further, drawing lines under their eyes".
