Most all tickets can be upgraded; if your ticket does not qualify, it should say so in the fine print on the back. Some complimentary, promotional, or special event tickets cannot be upgraded.
As wdwrich indicated, you can add days to your existing ticket, but it's going to have the same add-ons as your original ticket. So if you have a two-day park hopper ticket, you can add a third day, and it'll now be and three-day park hopper ticket. Likewise, if you have a two-day non-hopper ticket, you can add a day and it'll be a three-day non-hopper ticket. The price of the hopper add-on is fixed (it's the same whether you have a two-day or five-day ticket).
The price to upgrade is a little less clear. It depends on where you bought the ticket and whether or not they qualify for price bridging. Unlike WDW, DLR is not as consistent with price bridging, so no one knows in advance if you're going to get credit for the actual amount you paid for the ticket or the gate price of the ticket. Assuming you get credit for gate price, the cost to upgrade from a two-day to a three-day ticket would be $48 per adult ticket and $50 per child ticket.