"deeper grasp" is correct and usable in written English.
It can be used to describe a thorough understanding or comprehension of something. Example: The professor's lecture on quantum mechanics gave me a deeper grasp of the subject.
In sunflower linen, the suit suggests a deeper grasp of luxury.
Even in its compromised state, the new design moves toward a deeper grasp of history.
Perhaps as a secretary of state he would be a highly professional status quo figure like Hillary Clinton, but with a deeper grasp of the opportunities available in the world.
After 8... Be7, a Lalic-Speelman game in Hastings at the turn of the year gave a positional advantage to White after 9 g3 a5 10 h4 a4 11 but, but Speelman had a deeper grasp of the situation and later won cleverly.
And for me, the genre gave me a deeper grasp of my mother tongue, even if only in the sense that I learned how to call someone a ho and talk about the universal phenomenon that is coke dick.
"Bologna on white," Lily accurately guesses, in a moment meant to reveal her deep grasp of human nature.
Yet his delivery lacked Sachs' gravelly weariness and what to me felt like a deep grasp of the characters.
"But a deep grasp of technology is becoming more essential across our resource in every department, not less".
And there has been little from European leaders, especially Mrs. Merkel, to indicate a deep grasp of the crisis and how to fix it.
The real life 'Q' would want me to say that we too enjoy – and, indeed, need – a deep grasp of gadgetry.
This would be a corrupt, undemocratic way to make decisions about the shape of our society even if those involved really were wise men with a deep grasp of the issues.
