Can I change plan in the middle of a billing period?

Yes, you can switch plans at any time, not just at renewal.

What this means for you

Moving up to a higher tier while you're already on a paid plan applies immediately, in place (no new checkout), and is prorated for the rest of your billing period, so you're only charged for what's left of it.
Moving down, including all the way back to the free plan, also applies right away, without going through checkout again.
Before you confirm an upgrade, a small estimate shows you the prorated amount (or credit) you'd see.
Enterprise is the one exception. It's arranged directly with the WorkMonitor team rather than switched to yourself.