Curiosity,
I've never interned with giant corporate but I have done multiple internships that would hire me back and I have corporations currently doing their best to recruit me so while I don't have direct experience I do have some insight.
The short answer is to make yourself indispensable. The competition is relatively low. Excelling in work ethic is under your control. Basically you want to do whatever intern job you're doing to the fullest. You don't have to be the best skilled but show that you have the potential to be better than the best (or just be the best). Have a positive go getter attitude with managers and executives, and take initiative in taking on more responsibility if at all possible.
At the end of the day all anyone gives a shit about is production for the business. If you're producing or have the potential to produce better than most or anyone else and you're excited to make these people money then they'll be worried about you working elsewhere.
Worse comes to worse most corporations are starved for any promising talent. When I look for internships and jobs my favorite method is to cold call companies I'm interested to work for and asking them when I can start. Not a ton of people have initiative and drive to go above and beyond in corporate america. Be that guy.
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