In run-of-the-mill organizations—that is, in the majority of cases, it might be something of a stretch to identify specific organizational cultures and systems of governance that allow sustainability to "thrive within", for example to drive biodiversity initiatives. This said, there may be something to be said for sustainability reporting: the first environmental reports were published in the late 1980s by companies in the chemical industry (that had image problems); another group of early reporters comprised committed small- and medium-sized businesses with comparatively "advanced" environmental management systems. Many large organizations now produce annual sustainability reports from a wide array of ratings and standards, including those the Global Reporting Initiative promotes. Examples of sustainability reports are at https://www.adb.org/documents/series/adb-sustainability-reports. Cynics will, rightly, have their say. Ultimately, we must do more and better with less, which has deep (and to many unpalatable) implications for sustainable consumption and production.
I'm not really into corporate-based conservation, but I'm aware of a resource that coul be of interest: http://www.wildlifehc.org/our-impact/corporate-success-stories/