Keep in mind you can choose to make your plan changes effective for the current date, backdate them to the beginning of your billing cycle*, or make them effective for your next billing cycle. Each of these has a different effect.
If you're moving to a higher plan and aren't at risk of an overage this month, it may be best to future date so you don't have any proration for the difference of your current plan and the new plan.
If you're moving to a smaller plan and wouldn't be over the new plan's limits, backdating is a good option as it could result in your next bill being lower than the new usual bill for one month.
You can also choose to switch your plan effective the date your making the change, which can result in proration in the form of a credit or charge depending upon if you're going up or down in plan cost.
You can change your plan via myAT&T on your computer, on your phone or tablet, or by calling customer care at 611 or 800-331-0500.
*Some tasks such as adding a new line, previous feature or rate plan changes, etc. limit the ability to backdate further than a certain date.
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Justin, thank you for the quick response. What I actually meant is, I am currently on a family plan with one family member, but I want to switch to another family members plan instead. Is that possible as well?
Yes, it is possible as long as that person does not have any grandfathered plans.
This is a user to user forum. I am a user, just like almost everyone else on the site.
Award for Community Excellence 2019 Achiever* *The views and opinions expressed on this forum are purely my own. Any product claim, statistic, quote, or other representation about a product or service should be verified with the manufacturer, provider, or party.