Could tigers, leopards, and jaguars coexist?

I’m exploring the ecology of my world.
I know that I want a big cat that only lives in forests like a tiger, and another that can survive deserts, grasslands, and forest like a leopard or puma.
I know that I’d prefer animals native to north and South America though I’d be open to afroeurasian cats. A tiger and leopard works perfectly, but as said I’d prefer cats native to the America’s.
A puma nearly perfectly replaces Pumas but nothing fits the forest dwelling tiger.
But what about the jaguar, I asked myself. As I looked into it, Jaguars aren’t exactly like tigers and they have characteristics from leopards, tigers, and even lions. They appear to occupy a unique niche not seen on other continents (could this be because of the absence of large predators like lions or tigers?)

That got me thinking, could tigers, leopards (or maybe pumas), and jaguars exist on the same continent in close together or similar biomes/climates? Jaguars could be further more water adapted, always hunting near water as well as forests, doing best in wetlands. Tigers could be less water adapted and reside in forests and areas with tall grass. Leopards (or pumas) could live in forests, grasslands, and deserts, while hunting smaller prey that leopards common indulge in.

So, could this be possible and what things may happen as result of the three cats living along side each other? Would jaguars and tigers often come into conflict?