How to access maximum volume of tweets using Twitter Streaming API, without firehose access?

Twitter is a popular source of data for many applications, especially involving sentiment analysis and the like. I have some things I'm interested in doing with Twitter data, but here's the issue: To get all Tweets, you have to get special permission from Twitter (which, as I understand it, is never granted) or pay big bucks to Gnip or the like.

OTOH, Twitter's API documentation says:

Few applications require this level of access. Creative use of a combination of other resources and various access levels can satisfy nearly every application use case.

Using the filter api with keyword tracking seems like something that would be a big part of this, but you obviously can't enumerate every keyword. Using a User stream on many User accounts that follow a lot of people might be an option as well, and I'm not sure if it makes sense to think about using the search API in addition.

So here's the question "What combination of other resources and access levels is the best way to get the maximum amount of data from Twitter"?