I think it could hurt your chances, but it depends on what kind of work you're applying for. If all the jobs are pretty much the same skill level, skill type, etc., and you could generalize easily about them, then you might be able to make it work.
I look at applicants to see a passion for the kind of work they would be doing with the job I'm offering, with the hope that someone with passion will not leave as soon as I get them trained and productive. That's one of a manager's fears. Managers put a lot of their own time and effort into training, so they hope to get some return on productivity for a good long time from that.
Multiple applications for different types of positions at the same company could make me question if you knew what would make you happy (workwise, not paywise), because if pay is all you're after, then a job that pays a little more will cause me to lose you as an employee.
I think you need to make a clear case for not just your skills, but what you get statisfaction from doing and use that to position yourself as a top candidate. Again, you might be able to do that across a few different jobs, but make sure you're representing yourself the same way for each, and just emphasizing the part of each job that is the SAME and that you would feel good about doing.
Hope that helps.