For international flights even if you didn’t book your trip in business, there is a way for a fairly inexpensive upgrade – 56 airlines are offering upgrade auctions/bidding via the plusgrade platform. Inexpensive meaning it most likely will be less than original business price. The good side is, for every flight system shows chances of your bid to be approved. The downside is – you will not know the outcome until 36-72 hours before the flight.

Here is the full list of companies allowing upgrade bids.