You will be subject to change fees ($300 on an international itinerary, IIRC--I don't know as I never change trips
) plus a fare differential (likely substantial, since they would add in the missing fuel surcharge plus any higher fare).
If you paid less than $300 for the ticket, you'd be better off throwing it away and booking a new one from scratch at the going rate.
If you have UA Premier Gold or higher status, you
might be able to do a rolling Same-Day Change (~22 hours at a time at max), but for there to be your fare class available on every single necessary change for a week straight is highly unlikely. If you don't have at least Gold status, then the SDC fee ($75, charged each time you SDC) would make that an unreasonable option as well.