generally, if you add a line you can purchase a phone for a two year contract price. If you add a line and use a used phone you are still responsible for the contract term you agree to at the time of the addition of the line.

only the new phone will have the promotional contract price.

Adding a new line actually doesn't affect your other two phones at all besides that they now share minutes with that third line. their contract is not extended, and neither is their NE2 date. This is why you can't get another discount on new phones for those lines since technically you're not doing anything to extend the contract.

However, you can add the new line (getting a new phone for that line) and then activate your backup phone on the new line, and activate the new phone on one of your lines (this is called a buddy upgrade). This would only work for one phone though.

Make sure where ever you buy the phone from doesn't have stipulations about the phone remaining ...
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In addition to what the others have said, you can activate your old phone without a contract and wait for the other lines to become eligible for upgrade, at which time you could upgrade all three. You'll find a company-owned store will be more than willing to add the line with existing equipment without a contract attached to it.