Quick note: we're assuming OP isn't buying Basic Economy here. Basic Economy does not allow changes without a non-refundable fee to convert it into regular economy.

But I wanted to double-down on this: in most cases, the fare difference between the old and the new itinerary will be the same as the fare difference would have been if you'd purchased the ticket the way that you wanted to fly ti in the first place, subject to real-time inventory differences. Routing UA flights through a different gateway -- changing FRA-EWR-AUS to FRA-IAH-AUS -- would generally not be a problem if there is inventory in your booking class. But changing to a different carrier can be another thing entirely. While some UA fares allow travel on Aegean (A3), not all do, and not all A3 flights may be included depending upon routing rules. If United.com is offering two itineraries at the same price, and one includes and A3 flight and one does not, then it's likely that you can switch from the non-A3 itinerary to that particular A3 flight without penalty later if the inventory remains open, but if you're seeing a big fare difference, or picking flights from A3's website and hoping to be able to change to them later even though you can't find them on United.com, that could be an expensive proposition.