You can upgrade your account on your own at any time, day or night!
When you approach your monthly message allotment a green banner will display at the top of the page giving you an option to upgrade if you choose. When you reach your account plan limit, you will then move to a pay-as-you-go system. Each text message sent over your plan limit will just be 3 cents per message and you will be charged for that on your normal monthly invoice date.
You do have the option to upgrade to the next level plan instead of paying overages and you can do that anytime under the Settings Menu. There is a tab for Subscription & Billing where "Upgrade Account" is clickable in green. This brings up a pop-up box that shows your options to upgrade. When upgrading in the middle of a billing cycle it will display your pro-rated amount to be charged and have you click to confirm this charge and change of plans. With one click you can update your plan on your own! Any time of day or night! Below is an example of what the pop up box would look like.
Please note that the counters reset on your billing date and that is also listed under Settings Account Overview.