Synonyms for Solicit (same or very similar meaning)
WordNet sense 1 (make amorous advances towards):
court, romance, wooWordNet sense 2 (make a solicitation or entreaty for something; request urgently or persistently):
beg, tapWordNet sense 3 (approach with an offer of sexual favors):
accost, hookFrom the ODE community, based on WordNetadd/edit