Minami-ke Okawari is an alternate adaptation of the same source manga by a different studio. I suspect many of the same core stories we saw in the first one will appear again in the second one but perhaps with a different approach taken to flesh out the details of the stories and a different animation style.

The company doing the animation for Okawari (asread) has a much smaller resume than the company that did it for the first series, other titles they worked on include Shuffle and Kiddy Grade 2.