would it be possible to have a hunting dog that was good for more than one kind of game if so what would it be

If you mean a dog that will fluh pheasant out of a field and a dog that will heel until sent out to retrieve down ducks over water than yes. Or if you mean a dog that trees coon or points quail, not usually. But i have seen stranger things happen.

So what kind of game are you looking to pursue?

Makes a big differance what type of hunting dog we would be talking about.

Might be one out there, but I never seen one.

I had a female beagle that of course ran rabbits,but also would flush pheasants.

when I was a kid, my dad brought home a little female beagle. She was about a year old. He had dis some work for a farmer and that was his payment I think. She would run rabbits and also flush grouse. You had to retrieve it as she wanted no part of that, but she was a good hunter and a great family pet. I think my dad even used her once or twice to track wounded deer. I never got to go on those escapades being too young,but remember him and his hunting buddys taking her out one evening during deer season with a leash and lanterns.