The phrase "multi-faceted topic" is correct and may be used in written English.
It is typically used to refer to a topic or idea that can be approached from multiple angles. For example, "The impact of climate change is a multi-faceted topic that has implications for the environment, the economy, and public health."
Nutrition is a multi-faceted topic, with some well-known knowns: inequities in access to and control of assets have severe consequences for women's ability to provide food, care, and health and sanitation services to themselves, their partners, and their children, especially their female children.
What has been the tone of voice or the angle related to challenging multi-faceted topics or widely covered news?
Real quaternion analysis is a multi-faceted subject.
This is the most comprehensive overview available anywhere on the broad, multi-faceted and complex topic of pain – and the rapidly evolving scientific and medical disciplines that seek to understand, assess and treat pain.
Comments from Brianna: Some of the challenges of writing this piece were that the topic is multi-faceted and complex.
AI is a multi-faceted and complicated subject.
I can see possibilities for topic modeling, discovery of multi-faceted relationships between cases, and mapping of changes in contract conditions, etc.
The president also made clear that he does not believe abortion is the only way to reduce pregnancies and that this topic is much more multi-faceted than it has been portrayed.
This paper presents a multi-faceted system based on five research-focused characteristics: topic, approach, method, unit of analysis, and reference discipline.
Solving the gender gap is a complex multi-faced issue requiring an equally multi-faceted approach.
The Prostate Cancer Risk Management Programme has circulated an information pack on this topic to GPs, but it is likely that a multi-faceted approach is required for the successful dissemination of this information to primary care [ 30].
