In Bensonhurst Brooklyn we played another version of boxball. We used 4 boxes and the pitcher threw the ball bouncing it in the 2nd, 3rd and 4th box in quick succession. The batter had to hit the ball back into the 1st box in front of the pitcher. Caught was out, out of the box was out. One bounce a single, etc. we considered the most advaced form of box baseball and the older kids were very good at throwing the ball in the 3 boxes with all kinds of spins and reversing bounces. You could almost have he ball grazing the ground by the third bounce and very difficult to hit.
The games we played that were offshoots of punchball or slapball depended on how many players were available. We called them triangle (3 bases) and squareball (4 bases) They were played the width of the gutter (street). There was a chalk square in front of the batter that the pitcher had to lob the ball into for a strike. The batter could slap any pitch.
Justballs was selling spaldeens as of a year ago.