Here’s my take: Are you qualified for the jobs? If you can honestly answer “yes”, then by all means, apply.
I’m basing my advice on a couple of important assumptions. Assumption #1: This situation is most common with larger organizations/companies where similar roles exist in different departments or divisions. Assumption #2: The recruiting function in larger organizations is usually done online and usually involves more than one recruiter. So this means that it’s not likely that the same person will see your resume two or even three times. Assumption #3: The website doesn’t contain any instructions to the contrary (i.e. applicants may only submit one resume, etc.). Assumption #4: You’re sending a different, targeted cover letter with each application/resume.
If you haven’t demonstrated that you’re qualified for the job, you probably aren’t going to get noticed no matter how many applications you submit. And what you think makes you qualified, isn’t always what they’re looking for. Have I confused you yet? What I’m saying is that you should do some important research BEFORE submitting your resume/application online. Yes. Research. Talk to people. Find out what they’re looking for, beyond what is described in the job posting.