escalate

verb4

1. •
   To increase (something) in extent or intensity; to intensify or step up.

   • Violence escalated during the election.
   • The shooting escalated the existing hostility.
2. •
   In technical support, to transfer a customer, a problem, etc. to the next higher level of authority

   • The tech 1 escalated the caller to a tech 2.
3. •
   To climb.

   • Thus, actually a prior uncounselled misdemeanor conviction may often prove to be a boon to one escalating the ladder of crime to the point where he has been convicted of a major aggravated offense. — 1975
4. •
   (rare) To move by escalator.

   • Escalator after escalator flowed up to the heights above, […] Dov escalated up beside me, scowling. — 2000