No, it should be two successful attack runs, no more.
You could have 20 successful hits, as long as they are clearly devided into 2 strings of blows. For instance, bopping someone around with zanzokens, and finishing with a blow that leaves them in a crater is one successful attack. Punching someone through the wall, then having them escape for a while, and then suprise drop kicking them in the face is two.