Volkswagen solved one big problem stemming from its diesel emissions deception, agreeing on Tuesday to pay up to $14.7 billion to settle claims in the United States.

But the final financial toll — once the company deals with a long list of fines, lawsuits and criminal investigations around the world — may well be far higher. The continuing fallout could leave Volkswagen vulnerable to billions of dollars more in expenses at a time when profit is already under pressure.

So far, Volkswagen has set aside 16.2 billion euros, or about $17.9 billion, for costs related to its public admission last September that its supposed “clean diesel” cars had been deliberately designed to cheat on air-quality tests. Matthias Müller, Volkswagen’s chief executive, said less than two weeks ago that the amount was adequate.

But the American settlement with the government and car owners will consume a big chunk of that money. And Volkswagen faces even more scrutiny in the United States and around the world, most notably as authorities pursue criminal investigations.