WordNet (r) 3.0 (2006):

fall into
    v 1: be included in or classified as; "This falls under the
         rubric 'various'" [syn: fall into, fall under]

Moby Thesaurus II by Grady Ward, 1.0:

65 Moby Thesaurus words for "fall into":
   accept, acquire, alter into, assume, attack, attempt,
   be converted into, be responsible for, become, bring down,
   bring on, bring upon, buckle to, change into, come round to,
   contract, embark in, embark upon, endeavor, engage in, enter on,
   enter upon, evolve into, fall in with, fall to, gain, get,
   get under way, go about, go at, go in for, go into, go upon,
   have at, incur, invite, lapse into, launch forth, launch into,
   lay about, melt into, move into, open into, pass into, pitch into,
   plunge into, proceed to, ripen into, run, run into, set about,
   set at, set forward, set going, set to, settle into, shift into,
   tackle, take on, take up, turn into, turn to, undertake,
   venture upon, welcome