Applying to PhD programs while pursuing a PhD
In most fields in the US this would be acceptable. An exception might be if you have accepted a grant that has some sort of termination clause that prevents it or makes it difficult. If you wind up leaving your current position you might have some ethical obligation to finish up some tasks if they affect others, but that is a separate question. 

In general, though, you can seek a better position for yourself. 

But you will also need to be able to explain to the new institution why you are leaving and why you are a good prospect for their program. Self awareness and learning are usually a good reason that (most) people will accept.