"continue broadening" is correct and usable in written English.
You can use this phrase to suggest that someone should continue to expand their knowledge or skills. For example, "Your education should not stop with the degree you have; continue broadening your understanding of the world by exploring different cultures and ideas."
Rather, I think that social conservatives need to continue broadening their agenda.
According to the prime minister, "we should remain the closest ally of the U.S., and as allies influence them to continue broadening their agenda".
"We should remain the closest ally of the U.S.," the prime minister told Britain's ambassadors and senior diplomats in January 2003, "and as allies influence them to continue broadening their agenda.
It's a trend that Wizards of the Coast seeks to continue by broadening the public perception of the brand.
Through perpetual reinvention, he has seen his influence continue to broaden and extend: music reviewer Brad Filicky writes that over the decades, "Bowie has become known as a musical chameleon, changing and dictating trends as much as he has altered his style to fit, influencing fashion and pop culture".
In a statement, Nickelodeon said it and Urban Commons "have mutually agreed to not extend the partnership," while "Nickelodeon will continue to broaden its recreation portfolio by partnering with leading hospitality companies around the globe".
"Tony is a great addition to CNN's team as we continue to broaden our coverage of news that impacts our audience's lifestyles".
On Friday, she said that step was "already yielding positive results," and she expected the sororities to continue to broaden their membership throughout the academic year.
Whatever path its members choose on that matter, a Green presence in City Hall would continue to broaden and enhance the institution's deliberations and debates.
