If your parents get you a cell phone and add it to their plan as an additional line, they are adding one more line to their bill, so additional means another or one more.

Even though they added an additional line to their plan, your parents might ask you to pay for the additional charges. That means they will see how much more your phone usage adds to their plan, and will charge it back to you. If you complain, they might say to avoid additional conflict, you can just get your own plan and pay all of the bills!

Definitions of additional

adj further or added

“called for additional troops”
characterized or produced by addition

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