Is the underlined expression common? If it is, is ‘your’ necessary?
Interacting with other people enables you to deepen your understanding of yourself.
Yes, you often see "deepen" with "understanding" like that. It's better with "your", but the other way is not wrong.
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Yes, you often see "deepen" with "understanding" like that. It's better with "your", but the other way is not wrong.