Looking on the internet deeply has found these results:

to deepen on is the most popular phrase on the web.

to deepen a topic 111,900 results on the web	to deepen on 180,400 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
It will deepen a sense of grievance and create new recruits for terrorist activity. So, professor, in addition to research I had requested, I allowed myself to deepen some topics and of course I brought entire bibliography... good. Commission funding for research and surveys on specific topics to deepen understanding of European VET systems and practices, and their links to the labour market and other education sectors; The Commission proposes to reinforce Member States' compliance with the SGP and to deepen fiscal policy coordination. This might provide a way to deepen relations with the southern Caucasus region. Sometimes research institutes are invited to deepen specific aspects around city development. Cohesion has been necessary to deepen the integration process.	It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

to deepen a topic

111,900 results on the web

to deepen on

180,400 results on the web

More popular!

It will deepen a sense of grievance and create new recruits for terrorist activity.
So, professor, in addition to research I had requested, I allowed myself to deepen some topics and of course I brought entire bibliography... good.
Commission funding for research and surveys on specific topics to deepen understanding of European VET systems and practices, and their links to the labour market and other education sectors;
The Commission proposes to reinforce Member States' compliance with the SGP and to deepen fiscal policy coordination.
This might provide a way to deepen relations with the southern Caucasus region.
Sometimes research institutes are invited to deepen specific aspects around city development.
Cohesion has been necessary to deepen the integration process.

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.