escalate

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

Violence escalated during the election.

The shooting escalated the existing hostility.

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.

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.

They escalated upstairs to the Mall coffee tables.

To move by escalator.

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

There were people just about everywhere, packing the garish fluorescent-lit corridors, riding in humming golf carts, escalating up and down escalators, floating along on those George Jetson moving sidewalk thingies.