Yes, and we are. For example, two types of stem cells (embryonic and induced pluripotent) are producing human cells that are already being used to test candidate drugs for toxicity. These stem cells are routinely used to produce human heart muscle cells, and because heart toxicity can be lethal, this process will save the lives of both animals and people. Other projects are looking into computer simulations of various sorts that can help reduce the need for research animals.
The federal government is looking into alternatives to animal research.