The phrase "deeper level" means going beyond surface-level understanding or investigating something more profoundly. It suggests looking into the underlying reasons, hidden meanings, or complex aspects of a situation or subject. Full definition
The personality profiles are used to match members based on deep levels of compatibility. (eharmony.co.uk)
On deeper levels of the psyche there is a kind of mystical participation in one another. (religion-online.org)
Work outs challenge and engage the muscle groups at at deeper level, while incorporating fundamentals for balance and flexibility. (theforumathleticclub.com)