Kobayashi variants
The most orthodox play here may be Black at a (Kobayashi fuseki), but this way for Black has also been common.
Top players have tried this black formation, too. Ideas for White from pro games are: at a, which meets with the taisha or one-space pincer; at b; or an interesting wedge variant at c (wedge - when the approach to 3-5 is possible, perhaps an idea of Yoda Norimoto).
Since this way of playing out a side with a white 3-3 point also gets a stone on the 10-4 point, it will be very like the Kobayashi pattern if White approaches the upper right corner. White's common next play is at a, as one would therefore expect.