The idiom to dig deeper means to try harder or to give more effort or resources to something. To dig further into something means to investigate something to a greater extent.

1. I decided to dig a little deeper into Katherine's background in an attempt to figure out what makes her tick.
2. As I dug further into my family history, I discovered some interesting facts.
3. My coach always encourages me to dig deeper when I feel like I can't push myself any more.

1. I thought that it was important we dug a little further into the issue of inappropriate behaviour in the workplace, so I commissioned a full-scale investigation to take place.
2. At first glance it may seem like the company is doing well financially, but if we dig deeper we'll see that it is mostly operating on borrowed capital.