To increase, enlarge, or intensify: e.g. escalated the hostilities in the Persian Gulf.

In relation to tech support.

Getting to talk to the manager, because the tech support person you are dealing with hasn't a clue.
The verb to escalate is usually intransitive, meaning to get worse: the Cuban Missile Crisis could have escalated, had the Soviets not backed down.

There is a degenerate transitive use, meaning to make worse: the situation in Northern Ireland was escalated by the intervention of troops.

Then there's the tech support/business jargon usage, which is just plain wrong. That said, referring something to the boss usually will make it worse.

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