There's an irritating trend in contemporary English wherein writers seem to think that "deeply" collocates with every verb and adjective. It often seems to be stripped of any meaning other than as an intensifier. Here's a collection of quotations from the recent New York Times articles I put together a couple months ago (I've been complaining about this for a while, now):
"Mrs. Clinton, a deeply competitive debater..."
"We watch how she gradually persuaded a deeply reluctant Don to accept her choice and help her"
"Key G.O.P. Donors Still Deeply Resist Donald Trump's Candidacy"
"Mr. Trump’s fortunes depend deeply on a wide array of financial backers"
On the other hand, I think getting to know someone deeply makes perfect sense (as an implicit contrast to knowing the shallow or superficial aspects of a person).