One option is to use a Twitter Data Reseller (e.g. GNIP) who can sell tweets.
Another option is to maximize your use of the API. Here are some tips:
1. Check Rate Limit Status for each API you’re use to make sure you don’t go over and when the rate limit resets (currently every 15 minutes).
2. Look at the parameters to make sure you request a count of the maximum number of tweets for that API. e.g. a count can default to 20, but you can set it to 200, depending availability and limits on the specific endpoint. This potentially reduces the number of queries you have to make.
3. Page your results according to the Twitter’s Working with Timelines guidance. Use SinceID and MaxID to make sure you’re only requesting new tweets. This could reduce requests by reducing the number of tweets you need (through increasing the opportunity to stay within max count) and reducing the number of requests by avoiding queries for tweets you already have.
4. Essentially, you want to examine endpoint parameters with a perspective for how to decrease bandwidth and reduce the number of queries you have to make.