I'm a frequent flyer on international flights. Basically, the economy class ticket is bought by the company and of course includes an economy class meal. I wonder if after booking the ticket there is a procedure for asking a first class meal or if I can ask for an upgrade of my meal while I'm on board the airplane. I'm fine with topping up the price difference(if there is such).
The answer is no, although some airlines will allow you to purchase a special economy meal.
Airlines do not allow their premium class offerings to be split up. You either purchase the whole package or you get none of it. The meal is probably less than 15 USD per person at cost, plus a similar amount per bottle of wine at bulk discount prices, but there's no way the airline will reveal that. Nor are they going to discourage people from buying first class by suggesting the experience can be replicated in separate, cheap pieces.
In any event, a first class meal is not heated on a pre-prepared tray like the economy meals are. Each course is individually prepared in the galley and then hand-delivered to the table. I don't even see how a typical first class meal would fit on an economy seat tray. The meal presentation is a big part of it: you will need at least one cabin crew member for every ten or so passengers, because it is quite labour-intensive. You can't replicate that in the middle of an economy cabin, you don't have the space in the galley and you don't have spare members of the cabin crew to do it.
To be honest, you are not missing much. I would suggest enjoying a good meal in an airport restaurant and skipping the on-board service. You will probably eat better than the first class passengers.