The phrase "also more deeply" is correct and usable in written English.
It can be used when you want to emphasize an additional level of depth or understanding in a discussion or analysis.
Example: "The research not only explores the surface issues but also more deeply examines the underlying causes of the problem."
Alternatives: "further in-depth" or "more profoundly".
"Yes, you are more free if it is your own," Ms. Sander said, but you are also more deeply responsible.
They are also more deeply concerned about how powerful people fight to grab control of the state and otherwise compete to exert influence over the rest of society (a left-wing perspective).
"But it is also, more deeply, a movie about its own nonexistence — a narrative that confronts both the impossibility and the desperate necessity of storytelling, and that short-circuits our expectations of coherence, plausibility and fidelity to lived reality even as it satisfies them.
When flying high, the birds flap their wings not only faster, but also more deeply up and down, to stay airborne.
Green product users not only held higher expectation of green sportswear's ability to perform well, but also more deeply considered the trustworthiness of its environmental claims, compared to non-green product users.
Specifically, it gives it the platform to integrate also more deeply with other software providers like Salesforce, an important part of how Vonage sells its services to would be customers.
Patients receiving lorazepam were also more often deeply sedated (Ramsay Sedation Scale score 5 or 6) than those receiving midazolam.
Serena also appeared more deeply affected than Venus by their sister's death in 2003.
The investigation that began this spring suggested that the oversight within the supply chain may also be more deeply compromised.
But also, and more deeply, there was the combination of curiosity, inertia and obedience that is the most common and perhaps the least understood motive for movie attendance.
Future research could also delve more deeply into excessive users across different social networks.
