I entered Thailand on a Non-O visa. After 90 days I got a 60 day extension (visiting family). I then got a 12 month work extension, followed by another 12 month work extension which will expire in June 2019. Will I be able to get a 60 day extension again? I have left Thailand twice since I got my first 60 day extension.

If you got a re entry permit before leaving and used this to enter using your previous extension this still counts as the same stay and you can't get a 60 day extension again.

If you entered using a visa and started a new permission of stay then you can get a 60 day extension.

It is one 60-day extension per initial entry with a visa (or per visa exempt entry). Entering with a re-entry permit does not allow you a second 60-day extension.