If some of the schools that you are applying to accept the Universal App, you can max out the 20-school limit on the Common App and utilize the Universal App where possible to go beyond 20.
My daughter did this and ended up applying to a ton a schools in Fall 2014 (in part because of CC-induced paranoia about her odds of getting in anywhere!).
Since she was applying for financial aid, the adcoms had access to information which made clear to them she was applying to lots of school. This didn’t really hurt her at the elite university level (where her success/failure was largely predictable based on her credentials), but I think it did hurt her with some of the top liberal arts colleges, which tend to be concerned about yield and which thus want to offer slots to applicants who seem deeply invested in their particular institution. As a result, she was waitlisted at a number of LACs which were–statistically speaking–“easier” to get into than were some of the universities at which she was accepted.
The moral of the story is to be judicious in the application process, particularly if you are seeking financial aid and are considering multiple LACs!