WordNet (r) 3.0 (2006):

ask for
    v 1: increase the likelihood of; "ask for trouble"; "invite
         criticism" [syn: invite, ask for]

Moby Thesaurus II by Grady Ward, 1.0:

70 Moby Thesaurus words for "ask for":
   abet, aid and abet, angle for, apply for, ask, beat about for,
   beg leave, bespeak, blackmail, call for, challenge, claim,
   clamor for, countenance, crave, cry for, delve for, demand, desire,
   dig for, encourage, exact, extort, feed, file for, fish for,
   follow, foster, give encouragement, go gunning for, gun for, hunt,
   hunt for, hunt up, impose, indent, invite, issue an ultimatum,
   keep in countenance, levy, look, look for, look up, make a demand,
   make a request, make a requisition, make application, nourish,
   nurture, order, order up, place an order, prowl after, pursue,
   put in for, put in requisition, quest, request, require,
   requisition, screw, search for, see to, seek, seek for, still-hunt,
   try to find, warn, whistle for, wish