Companywide Edit Permission

Our company is broken into many teams, based largely on geography, however it’s not uncommon to collaborate with individuals from a different team.  When doing so it would be nice to have the option setting permissions to “Can Edit” for the entire company but it appears to not be an option.  We are aware that we can use a sharing link but those can accidentally be forwarded to people outside of our organization and thus unintentionally giving them more access then we would like.  Being able to give the entire company editing permission would be a better alternative for us.