You definitely can make your highest gear higher by using bigger tires, BUT the differences are small. Let's look at the numbers objectively:
Running a 32x11 as your highest gear on a bike with 700x44 wheels, you are talking about a top gear that is roughly 81 gear inches. Pedaling at 60RPM you'll be going 14.5MPH. Pedaling at 110RPM, you'll be going 26.6MPH. 81 gear inches is not that high a top gear.
Many cyclists complain that they spin out at 81 gear inches, and those people self identify as mashers. They like to push hard at low RPM. They don't want to pedal at 110RPM, but they want to go faster at lower cadence. That's cool. Get higher gears to do it.
Going from a 32 to a 34 increases that top gear by about 6% to about 86.5 gear inches. Pedaling slowly at 60RPM, you'll be going about 1 mile per hour faster, 15.5MPH. That's a small improvement
Going from 44mm tires to 55mm tires increases the wheel diameter by 20mm. That's about a 3% increase in diameter, so it increases the gear inches by about 3% to about 89 gear inches. It's about HALF the benefit you got from switching the chainring. Now mashing at 60RPM will make you go another half a mile per hour faster, to something like 16MPH.
Hypothetically if you could switch to a SRAM Eagle cassette which is 10-52, then your top gear would jump up by ~10%. In other words, switching from an 11T to a 10T cog would make more of a difference than changing both the chain ring and the tires. That's simple, but it's expensive.
If you made all of the above changes, we're talking about an 18% increase. Hypothetically if you could train yourself to pedal 20% faster, then you'd make more of an impact and do it for free. Pedaling faster is free if you are able to do it. Many claim that spinning is more efficient also. Many claim that they are far more able to spin when running shorter cranks. If you are already a spinner and already maxing out at 26MPH or faster and need to go still faster, then higher gearing is the way to go. Best of luck on all of it.
Bill Lindsay
El Cerrito, CA