The phrase "increasingly longer" is correct, and it is commonly used in written English.
For example, you could say, "The lines at the store are getting increasingly longer every day."
Indeed, consumers are taking on loans with increasingly longer terms.
Attached to a harness, he worked on his stamina, in increasingly longer, speedier bursts.
The statistics show that those convicted for terrorist offences are getting increasingly longer sentences.
All-audio materials containing lessons in which the listener is asked to recall previously learned material at increasingly longer intervals.
As the family grew, so did its Airstreams; the Fabers bought a Chevrolet Suburban to tow the increasingly longer trailers.
For each stress level, a series of creep-recovery tests were performed on single specimen for increasingly longer durations from 1 to 24 h.
Similar to training for a running marathon, you may train your body for an exam marathon with increasingly longer practice exams.
As with Ginsberg's most famous shot, of Jack Kerouac standing on the fire escape, subsequent captions built on one another and got increasingly longer with each re-print.
Patients with OCD characterized by excessive washing may be asked to dirty their hands and wait with a therapist for increasingly longer intervals before cleaning up.
Instead, re-study the essentials after increasingly longer periods of time — once an hour, then every few hours, then every day.
The bad news is that Medicare, as constituted, is simply not capable of underwriting an increasingly longer portion of our lives.
