Yes, I've used Amsoil 10w-40 in my machine after the engine was broken in. It is the best possible lubricant you can use. Go to their website and look at the numbers. Mobil 1 is your second choice.
Do not use dinosaur sludge like Castrol, Pennzoil, Kendall, Quaker State, Valvolene, etc. These parafin based oils will sludge up.
These dinosaur oils are not used in turbine aircraft engines because they will not stand up to the heat. Oils like Amsoil and Mobil 1 are used in aircraft engines today.
Beware of the term "synthetic" in popular oils. These are not PAO based, and are really petrolium (dinosaur) oils.
By the way, do not use Amsoil or Mobil 1 during engine break-in, or the rings won't seat properly. You want high wear during break-in. After break-in, you want to minimize wear, friction, and heat. The suggested breakin distance is 1500-2000 miles. Run the original oil 750 miles then run the second 750 miles on the Suzuki dinosaur oil. Change filter at every oil change. Then flip to a real synthetic. You can run the synthetic 1500 miles, change it, and keep the old oil and use it in your lawnmower.
The Amsoil will protect the cam chain better too, so you can go a lot longer without worrying about that as well.

going to get the Amsoil 10w-40 they have that. I have to go two towns over to get the mobil 1.  So Amsiol wins for my bike this time around! Plus it is close.  that is what happens if you live in ME. you have to go to a few stores be for you find what you need, even for a dam jar of peanutbutter.

The motorcycle-specific Mobil-1 is >$8/quart at my local Wal-Mart.