"deepened their work" is correct and usable in written English.
It generally refers to furthering one's knowledge or understanding of something. For example, "As the class progressed, the students deepened their work by exploring more complex concepts."
The men improved their works and deepened their trenches.
At a special ceremony, Dr. Timothy P. Shriver, Chairman and CEO of Special Olympics, and UNICEF Executive Director Anthony Lake pledged to deepen their partnership, working more closely together to combat the legal, social and physical barriers that exclude children with disabilities from full participation.
Like it or not, the primary beneficiary of research funding is the researcher, who has managed to deepen their understanding by working on a particular dataset.
And while we shouldn't expect them to find a smoking gun, we can hope that their work will deepen their understanding, and ours, of how much the government knew about the terrorist threat that was at our door.
To complement this desk work and deepen their understanding of how and why different legal norms evolve the authors conducted 19 in-depth key informant interviews with actors engaged with three stakeholders; the European Union, the United States and Belgium.
Meanwhile, the company had also been working on deepening their partnership with Microsoft, which invested in the 2015 round (along with rival Salesforce, which led that round).
Through SproutEd's communication and organizational tools, students can work together to deepen their understanding of academic topics and effectively manage their time.
Admirers of any classic work rightly wish to deepen their knowledge of the revered object, and the amplified edition provides a starting point.
All storytellers, no matter what their experience, are likely to go away with a new understanding of their writing process that will deepen and nourish their work".
