You might think that in big firms, applying to multiple openings at once ups your chances of getting a nibble. Career counsellor Brian McCullough suggests that every firm has someone looking over resumes, and they're not going to like seeing your multiplicity.
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On a general level, hitting a company for multiple positions at once makes you look, well, desperate. But for most jobs, it also nixes the idea that you're a particularly great hire for any one position:
More than that, the hiring manager might feel you're unfocused. As I've said many times, when hiring someone, the company is looking for the exact right person to fit their exact need. They want to feel like you'll fit in like a puzzle piece. If you show up saying, "Hey, I'll do anything, just pay me!" it sort of takes away from that feeling.
The solution, McCullough suggests in his TheJobBored blog post, is applying once, waiting to get word back, then applying again for a later, different position. Have you seen different, and found resume carpet-bombing to be effective?