The phrase "advancing this idea" is correct and usable in written English.
You can use it when discussing the development or promotion of a particular concept or proposal.
Example: "In our next meeting, we will focus on advancing this idea to ensure it gains traction within the organization."
Alternatives: "promoting this concept" or "furthering this notion."
When my colleagues and I started our own company, we advanced this idea a step or two.
We started to advance this idea in Quebec City, as a matter of fact, in 2000 with the Free Trade Agreement of the Americas.
"Not only are they not asking to advance this idea," he told Israel Radio, "they sat with me to see how to block it if it is raised by other players.
To advance this idea, the Reagan administration in 1987 abandoned the "fairness doctrine" that required media to present factual information and balance opposing viewpoints, giving free range to rightwing talk radio shock jocks such as Rush Limbaugh who pushed the idea that business regulation and social welfare policies destroy American liberty.
Instead, figure out what you can do, today, to advance this idea using only the resources you have.
Through debate and discussion, the Society aims to advance this idea on campus and among business leaders.
Going forward, there should never be an instance in which Buchanan is allowed to advance this idea without being immediately asked to reconcile his contention with this case.
To advance this idea, it would be valuable to examine whether the observations in the laboratory with the evolution of tamoxifen drug resistance apply to other SERMs and to breast cancer cells that have adapted to oestrogen deprivation, that is, as an expression of resistance to aromatase inhibitors.
Although, the name emphasizes double-strand breaks and we advanced this particular idea because of data obtained in double restriction enzyme selection, the mechanism also appears to be used to repair stalled forks (Constantino et al., 2014).
