In most cases I don't recommend doing so.
Instead, I think you should piggyback on your organization's existing social media. They've already got the "likes". Why try to start something from scratch? It's too hard, and you'll be competing with your pals in the Social Media Department who can spend all day working on building their Facebook community.
By the way, I think the real underdog for complementing your personal, face-to-face relationships in major gifts, is really LinkedIn. Check out this blog post to learn more about how to use that. There's a link to a cheat-sheet I created (all the way at the bottom).
Also, don't forget that you can actually advertise to your Facebook supporters while zeroing in on certain demographics. You can do the same on LinkedIn and Twitter... Instagram too!
And, finally, you should check out your profile on Glassdoor. Major donors might do that these days. If your reviews are bad, your leadership ought to seriously consider making changes. Here's MarketSmart's Glassdoor page.
In the end, if you really want serious results, the key is to step back and develop a really smart strategy. Otherwise, you'll just be spraying stuff around, and that's usually pretty ineffective, as well as, time-consuming.
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