"understand more deeply" is a correct and usable phrase in written English.
You can use it when you are trying to express that someone needs to learn about something in more depth. For example: "By doing more research, she was able to understand the topic more deeply."
He helped us to understand more deeply.
They understand more deeply what has happened to them.
Every day I understand more deeply how violent we are.
"They speak the same language," he says, observing that central bankers "understand more deeply than perhaps anyone else where other countries are coming from".
But it is also an attempt to help us as Catholics understand more deeply our mission by coming to listen deeply to the experiences of our brothers in El Salvador and the stories of the people of El Salvador".
The "theology of religions" (analogous to the "history of religions") has moved in the direction of dialogue, which sometimes simply refers to mutual acquaintance in charity so that people of differing faiths can come to understand more deeply the meaning of each other's religions.
Stevenson understood more deeply and clearly than most the fascination of the dark side, the allure of unreason and criminality.
And the force of his moral and intellectual progress can now be understood more deeply than ever before.
Thinking about the performance afterward, I understood more deeply that building a major orchestra isn't a matter simply of gathering the best players from the leading conservatories and paying a celebrity maestro millions to lead them.
It was a prayer that I understood more deeply last year, when I built a sukkah on the balcony of my apartment in Jerusalem, shortly after the start of the current intifada.
Reading Ah, Wilderness! again after working on Happy Days, I understood more deeply Richard's reliance on Khayyám and other poets and political writers to help him through the wilderness and to express the tumult of new emotions he is feeling.
