To Beat The Band Meaning

(idiomatic) Very vigorously; at a frantic pace; to a high degree; in large quantities.

Example: 1917, Jack London, Michael, Brother of Jerry, ch. 7,
  Fifty dollars gold 'd buy beer to beat the band—enough to drown me if I fell in head first.
1921, P. G. Wodehouse, The Little Warrior, ch. 7,
  Last time I saw you, you were a kiddy in short frocks, running around and shouting to beat the band.
1922, Peter B. Kyne, Cappy Ricks Retires, ch. 54,
  You rile me to beat the band sometimes, Skinner.