Checking against all static boxes

var xResolution = 1, yResolution = 1;

for (var i = 1; i < boxes.length; i++) {
  var newXResolution = resolveCollisionX(player, boxes[i], dX, dY);
  var newYResolution = resolveCollisionY(player, boxes[i], dX, dY);

  xResolution = Math.min(xResolution, newXResolution);
  yResolution = Math.min(yResolution, newYResolution);
}

player.x += dX * xResolution;
player.y += dY * yResolution;