There is a saying, if you keep doing the same thing over and over, don't expect a different outcome.
It sounds like you are operating under assumption that getting an internship should somehow put you in a special category where you magically end up with a job offer. But here you are, on your last internship and the assumption hasn't panned out twice already. Time to change the approach.
If you want a job with a company, as an intern you might be a better fit than someone off the street. But being qualified for a job and securing an offer are different things. If you are more qualified but less proactive, are your chances still better? So, you need to be at least as proactive as the most proactive applicant off the street. Do not just sit out the internship waiting for magic to happen. Water does not flow under an unturned stone. So, leave no stone unturned (gently). In other words, during your internship, spend time to systematically research the current job openings in various organizations, departments and units of the company (e.g. IT, Biz Ops, etc).
Cast the net broadly. Don't lock yourself into THE department where you think you are best fit. Whether you are a fit or not will not be up to you to decide, but to the hiring manager. Consider jobs that may be only a 50% or 75% fit with your skills from your perspective. Who knows, maybe all the other applicants for those positions are even less of a fit!
So, do your homework. Understand the kinds of positions the company has in different units, research them. Teach yourself to talk about the organization like you've been there at least a year. This may be a tall order, but you are under a deadline. You will probably have access to company intranet and all sorts of shared folders on the LAN, insider policies, HR manuals, etc. Use these resources.
Once you feel you can make some educated moves, begin applying for these positions. Your goal is not to get the one and only job at the company that is a perfect fit for you, in your opinion. Your goal is to get a foot in the door and create a stronger negotiating position for yourself by the time your internship nears conclusion. The worst that can happen is you'll get turned down - well, at least you tried. Or, you could get an offer for a less-than-perfect fit job. But at least you will have AN offer, which you can then choose whether to accept.
Hiring probably runs on a 2-3 month lag. So by the time the internship is up (assuming you will have graduated or will be really close to graduating at that point and can take on a job), you want your application to be well into the hiring process flow.
If you do get some interviews in other units, go through them and emphasize the experience you are gaining in your internship (which of course needs to be front and center on your resume). Exhibit your understanding of the company from the inside, which an application off the street is less likely to have. Insider knowledge is your competitive edge, so use it.
Think about what is a better situation to find yourself in at the end of the internship: having an offer with a different department as leverage to use in negotiations with your current unit/team about a possible job, or having no leverage and facing the possibility of yet another no-offer outcome?
For the management of your unit, knowing that someone else in the company is interested in bringing you on board might be a pretty big turn-on and might help them realize that you are not just a regular expendable intern but could be worth a closer look. Worst case, they won't care and won't be trying to recruit you. In which case you probably would not have wanted to stay there anyway.
Finally, I would encourage you to approach your new colleagues with a learner's attitude - don't be too in-their-face "hire me please" - this turns people off and they might see you as competition. You need to walk the line between being excited and interested in the company on one hand, i.e. curious, but not desperate. You need to be a little hard-to-get, mind-your-own-business. Again: curious, but not desperate. This is confidence. Even if you are not, act it. Everyone acts in the workplace. So, develop a "part" for yourself and act it consistently. Good luck!