They can work long hours to support a cause they believe in.

为了支持自己相信的某个事业，他们可以长时间的工作。

youdao

I was more than happy to lend my support to such a good cause.

我非常乐意给这样美好的事业提供援助。

《牛津词典》

They are raising a fund in support of this good cause.

他们正在为赞助这一有益的事业而集资。

youdao

Studies support the theory that there are several causes, instead of a single environmental cause or genetic problem.

VOA: special.2009.01.06

Education is a powerful tool to bring awareness and support to a cause.

WHITEHOUSE: Champions of Change Blog

This commemoration does not seek to coordinate funds toward a particular charity or to direct volunteers to support a specific cause.

FORBES: Is #GivingTuesday A Keeper? (Hint: Only If It's Open)

That said, large organizations must sometimes simplify and amplify their messages when making fundraising appeals or launching petition drives or campaigns to build grass roots support for a cause.

FORBES: Fear and the Killer Robots Meme