This is an "oldie but a goodie".
When someone likes one of your posts but does not like your page, you can invite them to like your page.
All you need to do is click the 'X People Who Like This' link underneath your Facebook page post.
From there, you'll see an option to invite people who haven't yet liked your page.
This feature does go buggy from time to time, but I've built some big audiences with it.
My no.1 piece of advice when using this strategy is to invite quickly - don't wait a month after your post and then go back and invite as people may have forgotten who you are.
* You can invite people up until your page reaches 100,000 likes.
* Don't fall into the trap of using an automated invite tool - this could get you in trouble with FB.
* Some people will probably find this annoying, your mileage may vary.
* This also works on boosted posts and regular ads (view your Ad URLs in Ads Manager) - don't miss out on these sources of easy likes.
I've grown some big Facebook audiences (that get great engagement) using this technique.
Any questions leave a comment below and I'll do my best to help you out!