I helped a department in a big corporation to grow their twitter account from 95 (I) to over 2k in 18 months through organic growth. That's four years ago when twitter was not as popular today. I provided resources for our audience and monitored the response to adjust my content. It took persistent work.

For my personal tweeter account, I noticed that 400 seems like a tipping point. After a solid 400, it grew really beautifully.