Accumulatively

adv. [f. prec. + -LY².] In an accumulative manner; collectively.

1657.  Reeve, God’s Plea for Nineveh, 144. We cry cunningly, artificially, disjunctively, by parts, by halfes, rather then cry really, accumulatively, mightily.

1870.  Smith, Syn. & Antonyms, Apiece, adv. Ant. Collectively, Accumulatively.