If the bill has been generated, it will be harder to do. If the bill has not been generated, go online change the minute plan to the next level. Then choose the change to be BACKDATED. Then change it back after the bill is generated.
With the new options, I think it automatically backdates the change if you are increasing minutes to cover an overage - that's the way it appeared to me when I was testing it.
Log in (as the primary) to your MyVerizon account, and click on the Account tab. On the Overview page is a blue text link that says "Change Minutes" - that will walk you through increasing the minutes to cover your overage and it will also tell you how much it will cost.
Thanks to the community members for your suggestions. Adding to what was stated, if your billing cycle has not closed, you want to make sure you change the calling plan by backdating it to the beginning of your current bill cycle. This way you have the full 1400 minutes allowance for your current calling period before the bill cycle closes. Additionally, your next bill will show the calling plan change with the you paying the difference between the 700 minute plan to the 1400 minute plan. The changing of the calling plan can help avoid overage charges as long as you did not exceed the 1400 plan selected based off your current usage. Bear in mind, the 1400 minute plan gives you free 10 Friends & Family numbers giving you added value. I would suggest staying on the better of the two plans depending on your usage of your phones.