In general, if your best alternative is to complete your trip on another line, neither your first line nor agency is obligated to transfer your ticket to a second line. To fly on the second line, you'd have to buy a completely new ticket. And if you're traveling on a nonrefundable ticket, at best, you could retain the cash value of that ticket, less an exchange fee, toward a future trip.
These are firm airline policies which an agency cannot override. Agencies such as Expedia simply abide by them. And when you have a problem such as this, your best bet is to pursue alternatives with the airline's agents on the spot, not the agency. If you get charged extra, it's because of the airline, not the agency.
Another reader, annoyed that his baggage didn't arrive on his flight, asked about delayed baggage:
"When my bag doesn't arrive on my arriving flight, what are my rights to compensation? Does the airline have to pay for interim expenses?"
The short answer, at least for most airlines, is, "They promise to get your bag back to you as soon as possible. If you're no longer at an airport, they'll deliver it to your home or hotel, and most say they'll cover interim expenses."
Here are the exact statements from their customer service plans or contracts of carriage:
Thus, most lines help out with essentials when your bag is delayed. But that's all you get – no additional cash, voucher value, or frequent flyer miles. And, obviously, that "reasonable expenses" limit means reasonable: No Armani suits or Dior gowns.
Another reader experienced a problem that I would not have expected: