Synonyms for Escalate:

n.

go through the roof, go up, double, add to. complicate, proliferate, aggrandize, augment, inflame, add fuel to the fire/flames, enlarge, amplify, build up, snowball, multiply, do more harm than good, build, aggravate, exacerbate, upsurge, burgeon, worsen, beef up, grow, swell, make matters/things worse, run up, extend, mount, soar, expand, wax, boost. escalate (noun)
intensify, step up.

v.

change (verb)
intensify, step up.
elevate (verb)
hoist, upraise, elevate, rise, rear, uplift, lift, raise, erect, levitate, exalt.
increase, be increased (verb)
step up, enlarge, expand, extend, grow, raise, magnify, rise, intensify, heighten, mount, amplify.
intensify (verb)
exaggerate, underline, accentuate, sharpen, magnify, stress, increase, intensify, deepen, heighten, emphasize.

Other synonyms:

beef up, upsurge, worsen, complicate, add to, exacerbate, aggravate. snowball, inflame, amplify, expand, augment, swell, enlarge, burgeon, wax. double, soar, proliferate, aggrandize, go up. multiply, mount, grow, boost. extend. build. increase
snowball.
intensify
exacerbate.
skyrocket
go through the roof.
step-up
step up.
Other relevant words:
complicate, proliferate, build, build up, burgeon, aggrandize, inflame, augment, multiply, amplify, extend, worsen, exacerbate, soar, go up, upsurge, grow, swell, double, beef up, mount, snowball, expand, enlarge, wax, boost, aggravate.