Yes: use "change flights" on the itinerary page for your old ticket, or call Reservations to reissue the ticket for a new itinerary. (I have done this very often.)

If you initially purchase a non-refundable ticket on continental.com, you can change your itinerary either online or through Reservations. You pay the change fee (usually $100 for domestic round trips) plus the difference in fares. The confirmation number stays the same, and 100% EQMs still post whether you use the site or the phone.

The "Change Flights" function on the website sometimes fails and sends you to the website support desk. This also works.

If the new ticket is cheaper than the old one, you still pay the $100 but get a travel certificate for the difference in the mail.

Very occasionally --this happened to me only once-- the fare rules on your original ticket specify that the new ticket has to be repriced using fares available on the original purchase date, so you can't get the cheapest new-ticket fare using your old ticket. (For example: you originally bought a W fare, U fares are available for new tickets, but you can only change your W to a more expensive B.) Sometimes a fare applies only between two specific cities, and you cannot use the credit to fly somewhere else. This seems to happen mostly with the price-matching I, W, and X fares.

The weekend specials (leave Saturday and return Mon/Tue to a hub) are an exception, being non-changeable.

I don't know how this works if partner codeshares are involved.