Sometimes they do, very successfully. Several prominent tech companies backed efforts to neuter patent trolls in the prior decade, to positive effect. Patent trolls are one instance where big tech's interests are largely aligned with smaller tech companies, as both hate them.
In the recent case of TC Heartland vs Kraft Foods, some large companies (Apple, eBay, IBM, Microsoft, Intel, Walmart) supported the effort to abolish being able to file patent lawsuits in most any venue (a concept which helped lead to East Texas becoming the capital of patent lawsuits in the US). Often you'll have big companies fight eachother in situations like that, as big pharma was on the other side of that, arguing in favor of being able to sue in any venue.
In the recent case of TC Heartland vs Kraft Foods, some large companies (Apple, eBay, IBM, Microsoft, Intel, Walmart) supported the effort to abolish being able to file patent lawsuits in most any venue (a concept which helped lead to East Texas becoming the capital of patent lawsuits in the US). Often you'll have big companies fight eachother in situations like that, as big pharma was on the other side of that, arguing in favor of being able to sue in any venue.
https://en.wikipedia.org/wiki/TC_Heartland_LLC_v._Kraft_Food...