That has never been mentioned for Blackbeard. And he said the marines, we know what marines are after in this chapter.
>We know Jinbe said Blackbeard is after DF users.
It's totally makes sense that if he hunts the Shichibukai since every one of them are DF users except for mihawk (Weevil is %99 DF user too). As for why mihawk, Shiryu might want to steal mihawk's special Kokutou Yoru sword as well.
I can't really see Boa or Mihawk joining him. Buggy is a possible case. Weevil has the highest chance but I don't know if he has a grudge against Teach or not since Teach was a former member of the WBP after all.