Collocations for escalate - verb

quickly, rapidly
gradually, steadily
Violence between the two sides has been steadily escalating.
The risks gradually escalate.

suddenly

into
The conflict could escalate rapidly into a full-scale war.

to
a small local disagreement that escalates to civil war

dramatically
Prices had recently escalated dramatically.

sharply
The cost of raw materials has escalated sharply.

to
The budget escalated to £32 million.

Escalate is used with these nouns as the subject:
conflict, cost, dispute, situation, violence, war