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Without knowing the site and the keywords (why is everyone so protective over these, even within this community??), it's almost impossible to say.
3 to 28 is quite a jump, but if the terms revolve around a trending news story or a seasonal term then that's not unusual at all. I would be happy to look further if you want to provide more specifics.
This isn't so much of a question as an offer
The Offer first, then the story. We are currently the target of a sustained negative SEO. This was only discovered in the last 3 or 4 days (Webmaster reports impressions down from 15,000 to 1,600!). I'm not asking for help, I believe we know what to do in order to combat it. My question is whether anyone at MOZ would like to use it as a real-life ongoing case study. We are not a new company and have never dabbled in black hat SEO. All current thinking suggests that this shouldn't have been possible given our age and reputation. A summary of our company/site below:
I'm not the best writer and I'm not that technical. I would gladly give the right person full access to anaylics, webmaster tools, sales reports, interviews. Given that this is still ongoing (and there's always a chance we might not recover!) I suspect this would make a great case study for the community given the right author.