"broaden support" is a correct and usable phrase in written English.
You can use it when describing an effort to obtain additional backing or approval from various sources. For example, "We need to broaden support for our plan to ensure its success."
If he wants, as promised, to bring change, he needs to broaden support.
Consumer groups have their own problems with the measure, saying too many accommodations have been made to broaden support.
We build and implement public/private partnerships to address the world's most pressing problems, and work to broaden support for the UN through advocacy and public outreach.
Critics fault Mr. Kress for his willingness to compromise, saying he knows the significance of each concession he makes to broaden support for the Bush plan.
His appointment is intended to broaden support for Somalia's weak transitional government, which is facing armed resistance from several radical Islamist groups.
At that time, it failed to win enough support among committee members who felt that too much additional spending had been added to broaden support.
This broadened support for emancipation might in turn pressure Lincoln to extend the proclamation beyond its wartime limits.
Support among civilians in areas in which the groups primarily operate also makes them more stable, by broadening support networks and helping them to safely retrench when needed.
Marine Le Pen has broadened support for the party by shedding the Front's antisemitic image and focusing more on issues such as unemployment.
The amendments could come in various sizes or shapes, in some cases written to wreck careful compromises that have broadened support for the bill.
The Somaliland president Dahir Riyale Kahin visited the US in April in the hope of broadening support towards the goal of recognition.
