Sometimes yes, and whether you can do it yourself depends on the airline and on the supplier the ticket was issued through. Some flight suppliers offer a change or reissue option in their API, so your staff can look up the existing booking, search new dates, see what the airline will charge and confirm the new flight from your own back office. Others do not expose that at all, and the only route is to raise a change request with the supplier service desk or contact the airline directly.
The airline and the fare rules decide most of this. Low cost carriers usually run changes through their own systems and a date change is often available straight through the API. Tickets issued on the traditional airline networks frequently need a proper reissue, which in many cases only a trained ticketing person can complete. The fare your customer originally bought matters as well, because the cheapest fares are often not changeable at all, and where a change is allowed the customer normally pays the fare difference, the airline penalty and any service fee you choose to add on top.
What we can do on your portal is make the process tidy either way. The booking screen can show a change option, your staff can see the fare difference and the penalty before they commit, the customer can be sent an updated ticket with the new reference, and the system keeps a record of who made the change and when. Where the API does not support a change, the same screen can raise a change request that goes to your team instead, so the customer is never left waiting with nobody looking at it.
Tell us which airlines you sell most often and we will check which of them allow changes through the API on your plan, then set up a manual request flow for the rest, and please confirm your own change fee and terms so they can be published on your site.