Well the easiest way to start would be if your wife's employer could allow the existing tickets to be cashed in, or just give her the cash equivalent of their cost, which you could then blend with your own funds to purchase the new tickets, in business class or premium economy, whatever.

Another possibility is using purchased frequent flyer miles/Avios to upgrade the economy ticket IF the economy ticket carries a fare classification that allows upgrades. You will need to know (a) the operating airline, if it's different from the airline named on the ticket, and (b) the fare classification of the current ticket. If it's a codeshare ticket, e.g. sold by British Airways but operated by Qantas, then the problem is greater because generally one can't upgrade flights operated on a partner airline using the frequent flyer program of a different airline, even if they're in the same alliance.

In the case where the selling and operating airline are the same, you'd then go to the operating airline's website and see if it's possible to use their frequent flyer "currency" (miles, Avios, whatever) for upgrades and what conditions and restrictions apply. If the existing ticket is in an upgradable category, then it's just a math problem. Figure out how many additional points you'd need for each traveler, find out the cost per point, and see if it makes sense. Note sometimes the issuing airlines will conduct "sales," such as one that recently ended in which you could purchase BA Avios for half price.

Note too that often upgrades will just be to the next cabin level, e.g. economy to premium economy, not a "two-step" jump to business. PE might be comfortable enough and is probably something you should consider.

Hope this isn't too confusing.