No minimum ticket length required. You can't max out over 10 days, including upgraded tickets. For example, if you have a 7 day ticket, you would only be able to add up to 3 days to your ticket, even if you used days.
Also to note, you can add extra days anytime within 14 days of first use--even if you have used all other previous days. In other words, if you had a 2 day ticket and went 2 days, but then decided to go a third day, you could come back anytime during those 14 days (for example, a week later) and add the third day. If you have tickets that are still valid (no expiration option), but were first used more than 14 days ago, you cannot upgrade them.
If you do add extra days, always use one day first. If your ticket was purchased before a price increase (which you obviously did since you already have tickets--even if just ordered and not picked up) and/or from a discount ticket broker, your ticket will automatically have the value of current gate prices IF you use the ticket first. Otherwise, you will only get credit for what Disney sold the ticket for (less than what you may have purchased it for if from a discount ticket broker). Now, if you purchased at current gate value, it isn't necessary to use the ticket first, but it is a good habit to have so you never make a mistake.
The current cost of a 2 day ticket is $168 at the gate. The current cost of a 3 day ticket is $232 at the gate. Upgrading would cost $64. The $8 differences do not start until you are going from a 3 day ticket to a 4 day ticket. A one day ticket is $85.
ETA: This does not assume park hopping, or any other, option.
